Question

If x + y = 12 and xy = 32 then find x square + y square = ?

Answer 1

x square +y square = 112

Answer 2

 x+y=12 ------Equation 1

Squaring equation 1 on both sides 

  (x+y)² = 12²-----Equation 2

(a+b)²=a²+2ab+b²

Now comparing (x+y)² with (a+b)² here a=x and b=y 

So Equation 2 becomes 

  (x+y)² = 12²

  x²+2xy+y² =12²

  x²+y² = 144 - 2xy----Equation 3

But in question its given that xy= 32 

So, substituting xy = 32 in equation 3

   x²+y² =144-2*32

  x²+y² =144-64 = 80