Math Olympiad | x²-y²=9 , xy=20 , Find x+y=?? 🤔

Math Olympiad | x²-y²=9 , xy=20 , Find x+y=?? 🤔 #Mamta maam #exponentialproblem #matholympaid
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[@ganeshdas3174]

x + y=9

[@user-go5sy7mu6q]

Perfect theorem

[@aruntiwari5714]

Perfect teaching method

[@ayhanozen8970]

X=5, Y=4

[@Maheshkumar-cw6un]

Its nice exponent equation

[@E.h.a.b]

(x-y)(x+y) = 9 //From [1]
(x-y)^2 (x+y)^2 = 81 //Square both sides
let (x + y)^2 = a
(x-y)^2 a = 81 -----> [3]
but we know that
(x-y)^2 = (x+y)^2 - 4 xy
(x-y)^2 = a - 4 * 20
(x-y)^2 = a - 80
(a - 80) * a = 81 -----> [4]
a^2 - 80 a - 81 = 0
a = ( 80 +/- √((-80)^2 - 4 (1) (-81) ) )/2
a = ( 80 +/- √( 4 * 1600 + 4 * 81 ) )/2
a = 40 +/- √1681
a = 40 +/- 41 = {81, -1}
x+y = +/- √a
x+y = {-9, 9, -i, i}

[@harshpathak2359]

Very good explanation

[@user-tc9cb8zh7b]

Full reasonable explanation

[@LaxmanKumar-yi4cv]

Perfect way to go

[@user-fz8rm8sy9m]

9

[@manojchaugule794]

good algebra math

[@mohinkhan2503]

❤❤❤❤❤❤❤❤

[@harikishan1900]

It's correct value

[@rehansaputra967]

X = 5, Y = 4
And X + Y = 9, or
X = - 4i, Y = 5i
And X + Y = i

[@arvindkulkarni6580]

X+Y will always be real number as far as I can imagine

[@SmartMoneyForexTrader]

Nice solving but "i" cannot be a solution because X^2 + Y^2 = Positive. It can never be negative. Hence the line you wrote, X^2 + Y^2 = +41 Or -41 can only be positive.
Hence the solution to the question is +9 or -9 ONLY

[@christianaxel9719]

if any x² or y² is complex the other one can be too resulting the sum in the "cancelation" of imaginary part.

[@niranjanchakraborty1139]

x+y=5+4=9.

[@SidneiMV]

x² - y² = 9
xy = 20
find x + y = A
(x + y)(x - y) = 9
x - y = 9/A
x + y = A
2x = A + 9/A
2y = A - 9/A
A² - 81/A² = 80
A² = 81 or A² = -1
*A = ±9 or A = ±i*

[@josemarino8787]

From y=20/x you get in the first equation x^4-9x^2-400=0. From here you get x^2 =25 or x^2 =-16.

[@ichdu6710]

also my idea. this is a more common way to solve such a pair of equation.

[@jeanlouis7561]

Why does she have to complicate a simple problem that a 5th grader can solve in less than two minutes?
The solution is x =5 and y = 4

[@MathSync]

“Fantastic explanation! I love how you break down complex concepts. I do similar math tutorials and challenges on my channel. Check it out for a fresh perspective on math problems!”

[@ganeshdas3174]

x + y=9

[@user-fz8rm8sy9m]

9