Question

If x+y=13 and x×y=36 then find the value of x^2+y^2

Answer 1

(x +y)2 = x2 + y2 + 2xy
13*13 = x2 +y2 + 2*36
169 = x2 + y2 + 72
x2 + y2 = 169-72 = 97

Answer 2

Heya User,

--> [ x + y ] = 13 ; xy = 36

=> [ x + y ]² - 2xy = 13² - 2*36
=> [ x² + 2xy + y² ] - 2xy = 169 - 72

=> x² + y² = 97 √√

Further, if you wish to -->

--> x² - 2xy + y² = 97 - 2*32
=> [ x - y ]² = 25
=> [ x - y ] = 5  ------> ( i )

And we also have, [ x + y ] = 13

So, solving for [ x ], x = 9 , y = 4 

Hence, you easily get your soln. Verified ^_^