Resolvi utilizando a lógica mesmo. Por exemplo: 7 elevado a potência 2 = 7 X 7 = 49, 5 elevado a segunda potência = 5 X 5 = 25, logo 49 - 25= 24, 7 X 5 = 35 e 7 + 5 =12.
Very easy to solve. No big formula required. X+Y = 12. XY=35. 35=35*1 or 17.5*2 or 7*5. First two are not suitable. So 7*5 =XY.. So X=7. Y=5. So 7*7=49. 5*5=25. 49-25=24. 7+5=12.
@@AshmanKhanna Not hit and run. Only some logic is applied. I applied the logic in case of XY=35 and got the value of X and Y. In competitive exams we do not have much time to solve these types of questions. Only logic should be applied for faster solutions.
35²=25×49=1225 It's a small mistake, but in (x,y)=(5,7),(-5,-7), x and y are reversed, so I don't feel like squaring 35. There is an answer, but you can do it without squaring x²-y²=24 ∧xy=35 ⇔ x²-y²=24 ∧xy=35 ⇔ x²-y²=24 ∧y=35/x ⇔x²-(35 /x)²=24∧y=35/x ⇔x⁴-24x²-7²・5²=0∧y=35/x ⇔(x²-7²)(x²+5²)=0∧y=35/x ⇔(x ,y)=(7,5),(-7,5),(5i,-7i),(-5i,7i) Of course I didn't calculate 35². Well, there is a rule like 15²=2 25 25²=6 25 35²=12 25 45²= 20 25 55²=30 25 65²= 42 25, so if you know that, you can calculate it right away.
Пусть (х+у)^2=а, возведем первое уравнение в квадрат (х+у)^2*(х-у)^2=576 а*(х^2+у^2+2ху-2ху-2ху)=576 В скобках мы прибавили и отняли 2ху а*((х+у)^2-4ху)=576 а*(а-140)=576 Дальнейшее просто
@@anime_pro_fan539 Я согласен, но так могут решить не все. Вообще это устно решается. х,у числа явно целые. 35 имеет два делителя 7 и 5 (1 и 35 не учитываем). Легко посчитать два решения (7,5) и (-7,-5) И есть ещё комплексное решение
@@user-ee7nw2rx9s ну я хз, как по мне с такой системой что ты написал решить смогут ещё меньше чем так как я написал, я такое решаю быстро, даже после титановый сетки в голове из-за перелома черепа, но сложные задачи и многое другое прокручиваются в голове медленнее чем раньше, хотя оно и понятно сломал себе череп из-за своей тупости и в ней шя титановая сетка
The question doesn’t tell you they’re natural numbers, of course you could guess get because it doesn’t make sense for them to be very complex, but “guessing numbers” is normally a no go for math Olympics
@@haylonARGI писать то надо но если устно просто нужно сказать ответ то достаточно сказать 7 и 5, а если, ну я то уже 2 года как школу закончил так что не могу сказать какие у вас учителя, но если учитель спросит ,,и это всё?" Значит учитель хочет от тебя ответ ±7 и ±5
Есть ощущение, что решить попроще можно было. А так... Как говорят у нас, в Африке, "пока одни изучают комплексные числа, другие в это время изучают автомат Калашникова" 😐
set u=x+y and v= x-y then u*v=24 but (x+y)^2-(x-y)^2=4*x*y=4*35 Therefore u^2-v^2=4*35, v^2=u^2-4*35. u^2*v^2=24^2 u^2*(u^2-4*35)=24^2 u^2-2*2*35*u^2=24^2 (u^2-2*35)^2=24^2+(2*35)^2=4*12^2+4*35^2 (u^2-2*35)^2=4*(12^2+35^2)=4*(35^2+12^2). but 36^2=(35+2)^2=35^2+2*2*35+2^2=35^2+140+4=35^2+12^2 Thus (u^2-2*35)^2=4*37^2 u^2=2*35+-2*37=2*(35+-37) u^2=2*(35+37)=144 or u^2=2*(-2)=-4
at 6:32 - x^2+y^2 = 5476 if you take roots, isn't everything already positive? How taking square roots from both sides gets you with +/-? Please explain...?
Another thing, even if the number are negative they are both negative, it's not possible for one to be negative and the other positive since xy=35. So the answer can be +/-12
sabe resolver uma conta bem parecida com essa ,não to conseguindo resolver, a conta é: x² - y² = 15 e o outro sitema de equação é xy=15 . o problema é muito parecido com o do video mas não consigo reslponder, quem souber resolver deixa a resposta ai
here it’s impossible to say for sure if we take the + sign, because 12 can also be obtained by 4+8, 3+9, etc., but if we take xy, then it’s clear because 35 is only in the case of 7×5 and this fits everyone’s requirements, but with + you can already have a bunch of options, and if 7+5 doesn’t immediately come to mind, then you’ll try 2+10, 3+9, 4+8, 11+1, etc. even -2+14, but with xy=35 it’s immediately clear because everyone knows the multiplication table from the age of 7
This question is prepared in a way such that the answer could be obtained by doing prime factorisation of 35 , using any other ways is just dumb way of solving and a matter of waste of time
sabe resolver uma conta bem parecida com essa ,não to conseguindo resolver, a conta é: x² - y² = 15 e o outro sitema de equação é xy=15 . o problema é muito parecido com o do video mas não consigo reslponder, quem souber resolver deixa a resposta ai
After seeing the equations squaring both numbers then subtracting from get results in 24 multiplying x and get 35 makes x=7 y=5 adding them up results in 12
ans. x=7. &. y=5 ,( no need to solve) so x+y=7+5=12.
L intéressant c est de faire la démonstration ,le résultat a peu d importance .
Not that simple
That's just sort of guessing!
35=7×5=>x=7 and y=5
No. The numbers might be negative too. (-7) and (-5).
(-7)×(-5)=35
2 2
(-7) - (-5) = 49-25 = 24
So, we need to solve.
Just looking at the factors of 35 it's clear that it must be +-7 and +-5, so +-12
12(X7,Y5)
7and5
Resolvi utilizando a lógica mesmo. Por exemplo: 7 elevado a potência 2 = 7 X 7 = 49, 5 elevado a segunda potência = 5 X 5 = 25, logo 49 - 25= 24, 7 X 5 = 35 e 7 + 5 =12.
Terlalu panjang..asal hafal kali2an cepat terjawab...x= 7 y=5
x + y = 12
8:04 everything was perfect until you started looking for the sqrt, after that I got disappointed
Very easy to solve. No big formula required. X+Y = 12.
XY=35. 35=35*1 or 17.5*2 or 7*5. First two are not suitable. So 7*5 =XY..
So X=7. Y=5. So 7*7=49. 5*5=25. 49-25=24.
7+5=12.
Bro you have used hit and trial method but we should use proper identity or logic which is shown in video
@@AshmanKhanna
Not hit and run. Only some logic is applied. I applied the logic in case of XY=35 and got the value of X and Y. In competitive exams we do not have much time to solve these types of questions. Only logic should be applied for faster solutions.
35²=25×49=1225
It's a small mistake, but in (x,y)=(5,7),(-5,-7), x and y are reversed, so I don't feel like squaring 35. There is an answer, but you can do it without squaring x²-y²=24 ∧xy=35 ⇔ x²-y²=24 ∧xy=35 ⇔ x²-y²=24 ∧y=35/x ⇔x²-(35 /x)²=24∧y=35/x ⇔x⁴-24x²-7²・5²=0∧y=35/x ⇔(x²-7²)(x²+5²)=0∧y=35/x ⇔(x ,y)=(7,5),(-7,5),(5i,-7i),(-5i,7i) Of course I didn't calculate 35². Well, there is a rule like 15²=2 25 25²=6 25 35²=12 25 45²= 20 25 55²=30 25 65²= 42 25, so if you know that, you can calculate it right away.
Пусть (х+у)^2=а, возведем первое уравнение в квадрат
(х+у)^2*(х-у)^2=576
а*(х^2+у^2+2ху-2ху-2ху)=576
В скобках мы прибавили и отняли 2ху
а*((х+у)^2-4ху)=576
а*(а-140)=576
Дальнейшее просто
И ты усложнил как и автор ведь тут чисто на логике можно решить xy=35=>x=35/y либо y=35/x=>x=±7 и y=±5
@@anime_pro_fan539
Я согласен, но так могут решить не все. Вообще это устно решается.
х,у числа явно целые.
35 имеет два делителя 7 и 5 (1 и 35 не учитываем).
Легко посчитать два решения (7,5) и (-7,-5)
И есть ещё комплексное решение
@@user-ee7nw2rx9s ну я хз, как по мне с такой системой что ты написал решить смогут ещё меньше чем так как я написал, я такое решаю быстро, даже после титановый сетки в голове из-за перелома черепа, но сложные задачи и многое другое прокручиваются в голове медленнее чем раньше, хотя оно и понятно сломал себе череп из-за своей тупости и в ней шя титановая сетка
12
Or you could have just got it from xy=35 x=±7 y=±5 x+y=±12
😉
The question doesn’t tell you they’re natural numbers, of course you could guess get because it doesn’t make sense for them to be very complex, but “guessing numbers” is normally a no go for math Olympics
😅7 и 5. Моментально ❗
-7 и - 5 забыли
@@haylonARGIну -7 и -5 не нужно говорить ведь это просто то же самое в отрицательном виде, ну а так да ±7 и ±5
@@anime_pro_fan539 нужно, это же тоже вариант ответа. Или, по-вашему, X² = 49 => x = ±7, то достаточно записать x = 7? Это не так.
@@haylonARGI писать то надо но если устно просто нужно сказать ответ то достаточно сказать 7 и 5, а если, ну я то уже 2 года как школу закончил так что не могу сказать какие у вас учителя, но если учитель спросит ,,и это всё?" Значит учитель хочет от тебя ответ ±7 и ±5
,12
Good luck sR❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤
7 x 5 = 35. Por lo tanto 7 + 5=12
X-7, y-5, 7+5=12
Put x=35/y and substitute in the other equation you can get both x and y and then x+y
no u cant lol
But actual time to solve ->30 secs in any exams
இவ்வளவு மெதுவாக செய்தால் பிள்ளைகள் பார்க்க மாட்டார்கள்
Задание интересное!
i ❤ Mathematics
x + y = 7 + 5 = 12
Я за несколько секунд нашла ответ Х+У=12, Х=7, У=5
Matematica trebuie sa simplifice lucrurile , nu să le complice! Doar dacă vrei să dovedesti ca sti toate formulele.
Есть ощущение, что решить попроще можно было.
А так... Как говорят у нас, в Африке, "пока одни изучают комплексные числа, другие в это время изучают автомат Калашникова" 😐
35= 7×5=>x=7 and y=5 😑
set u=x+y and v= x-y
then u*v=24
but
(x+y)^2-(x-y)^2=4*x*y=4*35
Therefore u^2-v^2=4*35, v^2=u^2-4*35.
u^2*v^2=24^2
u^2*(u^2-4*35)=24^2
u^2-2*2*35*u^2=24^2
(u^2-2*35)^2=24^2+(2*35)^2=4*12^2+4*35^2
(u^2-2*35)^2=4*(12^2+35^2)=4*(35^2+12^2).
but 36^2=(35+2)^2=35^2+2*2*35+2^2=35^2+140+4=35^2+12^2
Thus
(u^2-2*35)^2=4*37^2
u^2=2*35+-2*37=2*(35+-37)
u^2=2*(35+37)=144 or u^2=2*(-2)=-4
-12,-2,2,12
X*y=35.
7*5=35.
7+5=12
X=7,Y=5
7+5=12
at 6:32 - x^2+y^2 = 5476 if you take roots, isn't everything already positive? How taking square roots from both sides gets you with +/-? Please explain...?
Another thing, even if the number are negative they are both negative, it's not possible for one to be negative and the other positive since xy=35. So the answer can be +/-12
For example if we have to solve for x in x^2=49, then x will be +-7 but √49=+7 only
Trivial x=7,y=5
Решаем в уме. х +у = 12.
7 + 5= 12
Risposta : 7. e. 5.
x+y=±12
Giải rườm rà vậy. X = 35/Y . Thay vào rồi giải phương trình bậc 2 thôi
12 or -12
Х=7 , У=5 от 35-24=12
X=25,,,,y=1
Method.
38
X+y=12
There is an easiest way to solve it!!
X=35/y and replace
Let
u = x + y,
v = x - у
Then
x² - y² = 24 => uv = 24 (1)
xy = 35 => u² - v² = 4*35 = 140 (2)
From (1)
v = 24/u (3)
Substitute (3) in (2)
u² - (24/u)² = 140
or
u⁴ - 24² = 140u²
or
u⁴ - 140u² - 24² = 0 (4)
From (4)
u²₁,₂ = [140 ± √(140² + 4*24²)] / 2 = [140 ± √(4² * (35² + 12²))] / 2 = [140 ± 4√(1369))] / 2 = [140 ± 4√(37²))] / 2 = 70 ± 2*37 = 70 ± 74
u²₁ = 144 => (x + y) = ±12
u²₂= -4 => (x + y) = ±2i
❤️❤️
12.
Why need to mention +_ even it is positive.
O X equivale a 7 e o Y a 5
sabe resolver uma conta bem parecida com essa ,não to conseguindo resolver, a conta é:
x² - y² = 15 e o outro sitema de equação é xy=15 . o problema é muito parecido com o do video mas não consigo reslponder, quem souber resolver deixa a resposta ai
There are no factors other than 7x5 for 35
So answer must be 7 and 5
Silly question
X=7 y=5 so x+y =12
x = ±7; y = ±5
x + y = ±12
here it’s impossible to say for sure if we take the + sign, because 12 can also be obtained by 4+8, 3+9, etc., but if we take xy, then it’s clear because 35 is only in the case of 7×5 and this fits everyone’s requirements, but with + you can already have a bunch of options, and if 7+5 doesn’t immediately come to mind, then you’ll try 2+10, 3+9, 4+8, 11+1, etc. even -2+14, but with xy=35 it’s immediately clear because everyone knows the multiplication table from the age of 7
This question is prepared in a way such that the answer could be obtained by doing prime factorisation of 35 , using any other ways is just dumb way of solving and a matter of waste of time
A resposta correta é 12
sabe resolver uma conta bem parecida com essa ,não to conseguindo resolver, a conta é:
x² - y² = 15 e o outro sitema de equação é xy=15 . o problema é muito parecido com o do video mas não consigo reslponder, quem souber resolver deixa a resposta ai
After seeing the equations squaring both numbers then subtracting from get results in 24 multiplying x and get 35 makes x=7 y=5 adding them up results in 12
24 в квадрате равно 496
Wrong method।
Полнейшая чушь.... Мой племянник 10 лет решил в уме за 20 секунд...Самый тупой препод...
Всё решается в уме по первой строчке все понятно.зачеи столько трудностей и писанины.кстати мне65
Eu resolvi de cabeça, xy=35, só 7×5=35.
12
12
12
12
12
12