I think there is a simpler route allowing you to solve the problem in your head without pen and paper. Notice that there is an obvious trivial solution x=0. In step two 2*sqrt(x)=x divide by sqrt(x) and you get sqrt(x)=2. Square both sides to get x=4.
I love little simple videos like this tbh. The simplest way I see it is to just show that x is a number such that 2*sqrt(x) = sqrt(x)*sqrt(x) and then match terms. This immediately implies that sqrt(x) = 2
Be careful because when "cancelling" sqrt(x) you are actually dividing both terms by sqrt(x), of course you can't divide by 0... which means it is a separate case... which fits the equation.
@oahuhawaii2141 you're right. That was definitely oversight on my part, as 0 is a solution to the equation 2*sqrt(x) = x, I was tunnelling on getting the sqrt(x) = 2
@matheusjahnke8643 I actually didn't do the cancelling in my head, I just matched the terms to see you have 2 times sqrt(x) and sqrt(x) times sqrt(x), which effectively is cancelling but as in my deduction I'm looking at the fact that the other term attached to the sqrt(x) is a 2, which would make them equal. I suppose its that thinking that caused the oversight
@higher_mathematics Please ignore the negative comments from the peanut gallery of self-absorbed parrots who likely have never done anything to advance the frontiers of mathematics, but act like your videos are beneath their proficiency level. I spent lots of years studying math and completely enjoy your channel, even when I might take a different approach. Don't like this channel, go start your own, maybe call it "Home of the 3rd Derivatives of Displacement" so you sound cool. Thank you Higher Mathematics!!
sqrt(x) + sqrt(x) = x 2sqrt(x) = x 2 = x/sqrt(x) [x = sqrt(x) * sqrt(x)] 2 = sqrt(x)*sqrt(x)/sqrt(x) 2 = sqrt(x) 2 + 2 = x 4 = x Another way of coming to the solution, great video regardless.
Число 4 не может считаться полным решением, в данной подаче уравнения. В изначальном уравнении фигурируют знаки квадратного корня, а квадратный корень из 4 может быть отрицательным
The square root of 4 is ±2 (-2) + (-2) = -4 For the equation to work, the actual square root plus the actual square root has to equal x 0 × 0 = 0 0^0 = 0 0 + 0 = 0 0 - 0 = 0 X = 0
So funny are those who found the solution in 1 second :D. The real solution is a... debate as several people have noticed. What if sqrt(4) is -2? So the debate is that the equation was badly designed. It should be: abs(sqrt(x)) + abs(sqrt(x)) = x
To everyone complaining it’s not “Higher”, he wrote
E A SY in The title.
Study Math but study grammar too!
2√x = x
(2√x)² = x²
4x = x²
x² - 4x = 0
x(x - 4) = 0
x = 0, x = 4
I think there is a simpler route allowing you to solve the problem in your head without pen and paper. Notice that there is an obvious trivial solution x=0. In step two 2*sqrt(x)=x divide by sqrt(x) and you get sqrt(x)=2. Square both sides to get x=4.
In math you have to write everything
So X is a number whose square root is exactly half its value. 4 is the only number which has this property.
But you missed x = 0 .
I watch these just cause of his nice handwriting
Proof it
This one's easy but I appreciate your channel!
Nice job, Euler.
I love little simple videos like this tbh. The simplest way I see it is to just show that x is a number such that 2*sqrt(x) = sqrt(x)*sqrt(x) and then match terms. This immediately implies that sqrt(x) = 2
But you missed x = 0 .
Be careful because when "cancelling" sqrt(x) you are actually dividing both terms by sqrt(x), of course you can't divide by 0... which means it is a separate case... which fits the equation.
@oahuhawaii2141 you're right. That was definitely oversight on my part, as 0 is a solution to the equation 2*sqrt(x) = x, I was tunnelling on getting the sqrt(x) = 2
@matheusjahnke8643 I actually didn't do the cancelling in my head, I just matched the terms to see you have 2 times sqrt(x) and sqrt(x) times sqrt(x), which effectively is cancelling but as in my deduction I'm looking at the fact that the other term attached to the sqrt(x) is a 2, which would make them equal. I suppose its that thinking that caused the oversight
Thank you for watching. What do you think about this question? Have a great day and love math!❤❤❤
Very Good explanation
basics
can we do like this: 2=x/sqrt(x) -> ^2 -> 4=x^2/x -> x=4
@@dimak76 Zero is also a solution
@higher_mathematics Please ignore the negative comments from the peanut gallery of self-absorbed parrots who likely have never done anything to advance the frontiers of mathematics, but act like your videos are beneath their proficiency level. I spent lots of years studying math and completely enjoy your channel, even when I might take a different approach.
Don't like this channel, go start your own, maybe call it "Home of the 3rd Derivatives of Displacement" so you sound cool.
Thank you Higher Mathematics!!
Higher mathematics ❌
Complexity mathematics✅
sqrt x + sqrt x = x
Square both sides.
x + x + 2x = x^2 [(a+b)^2 = a^2 + b^2 + 2ab]
2x + 2x = x^2
4x = x^2
4x - x^2 = 0
x(4 - x) = 0
4 - x = 0 [divide both sides by x]
4 = x. Ans.
sqrt(x) + sqrt(x) = x
2sqrt(x) = x
2 = x/sqrt(x)
[x = sqrt(x) * sqrt(x)]
2 = sqrt(x)*sqrt(x)/sqrt(x)
2 = sqrt(x)
2 + 2 = x
4 = x
Another way of coming to the solution, great video regardless.
Interesting😂😂😂😂😂😂😂😂😂😂😂
√x+√x=x
=>2✓x=x
=>4x=x²
=>4x/x=x²/x
=>4=x
rad X + rad X = X or
2 • rad X = X or
4 • X = X² or
4 = X
Число 4 не может считаться полным решением, в данной подаче уравнения. В изначальном уравнении фигурируют знаки квадратного корня, а квадратный корень из 4 может быть отрицательным
из квадратного корня никогда не выходит отрицательное число, это невозможно.
√4 = 2; никак не -2, открой учебник за 8-ой класс
Если икс в квадрате равен 4, то икс- это плюс минус два. Не нужно путать одно с другим. Не позорьтесь.
sqrtx + sqrtx = x
2(sqrtx) = x
2(sqrtx) = sqrtx*sqrtx
2 = sqrtx
2^2 = x
x = 4
√x + √x = x
2√x = x
4x = x²
4 = x
Thats more simple
Best answer by far!
Please don't call it Higher Mathematics 😂
He wrote: “Fun and E A S Y” in The title.
He also say in the video, that it's easy, but some students are confused
Some people didn't develop reading skills
2√x = x
Let t = √x
2t = t²
t² - 2t = 0
t(t - 2) = 0
t₁ = 0, t₂ = 2
x₁ = 0, x₂ = 4
If there are more square roots of x, then x1 = 0 , x2 = (number of square roots of x) ²
I did it on my head
Also the answer is very easy to assume
2 root x = x
(2 root x) squared = x squared
4x = x ^2
4= x^2/x
4 = x
The square root of 4 is ±2 (-2) + (-2) = -4 For the equation to work, the actual square root plus the actual square root has to equal x
0 × 0 = 0
0^0 = 0
0 + 0 = 0
0 - 0 = 0
X = 0
Sqrt(x)+Sqrt(x)=x x=0 x=4
I don’t have to think about it.
I didn't even need to start the video. I immediately see that x = 4.
How you became at that level
But you missed x = 0 .
Very easy.
√x+√x=x
2x=x
2x÷√x=x÷√x
2=√x
X=2^2=4 (This sum is not do hard. It is a class 8th-9th calculation in India😊😊😊
Have a geometry problems?
It is just simple. Not higher math but elementary math.
X5 -1 =0, so x5 =1. Then x = 1 . Simple
2*√x = x
√x*(√x - 2) = 0
√x = 0, 2
x = 0, 4
Take note that square root of 4 is plus or minus 2! Negative 4 is not equal to 4. How do you handle that?
If you plot y=2rootx and y=x. You will see that the solution is solid. x = -4 does not appear anywhere. Good question though.
I don't know where i can use this stuff 😞
Preschool Olympiad ?
Similar question: solve x+x=x*x. Even easier 😉
x = 2 and x = 0
When you say "Prove" don't you mean "Check"?
Before I watch an overstate solution, I say x = 4 and that's it.^^
But you missed x = 0 .
X=4
x 4 easy
4
x = 0, 4
You could have written the fourth step as
4x=x^2
4=x^2/x
4=x
x=4
But both are same🤷♂️
But this is even easier
It's a quadratic equation it always has 2 answers they may be same,real or non real
@@GigaNoobs-k1j yeah i know but we get the answer right?
@@praveen.m2591 you only got one of the 2 correct answers
@@GigaNoobs-k1j my bad
Your so called prove is not really a prove, but a check, to prove it I would use the properties of monotone functions
x=0
So funny are those who found the solution in 1 second :D. The real solution is a... debate as several people have noticed. What if sqrt(4) is -2? So the debate is that the equation was badly designed. It should be: abs(sqrt(x)) + abs(sqrt(x)) = x
The real numbers has only one solution when u sqrt them. sqrt(4) can only be 2
x=0😊
x = 0, 4
Don’t call it higher math
Answer is X=2; X=0
Its obviously 0
But you missed x = 4 .
Bro in india students of age group 11-12 will solve 💪tougher question than this
When x=4, √x=√4=±2. When we take x=-2, then -2+-2=-4≠4. What do we say?
0;4
not gonna follow this anymore.
{x+x ➖ }=x^2 (x+x ➖}=x^2 {x ^2+x^2}= x^4 x2^2 (x ➖ 2x+2),
???
@@oahuhawaii2141 hello
What the fuck it is
😅4 моментально ❕
0?
x = 0, 4
X = 4
4
4
4