help pls Solve x2 y2 113 x y 15SolutionGiven that x2 y2

help pls

Solution

Given that x² + y² = 113 -------- ( 1 )

and           x + y = 15 ------------ ( 2 )

Now squaring on both sides of ( 2 ) we get

( x + y )² = 15²

x² + y² + 2xy = 225 ---------------- ( 3 )

from ( 1 ) we have x² + y² = 113 substitute in ( 3 ) , we get

113 + 2xy = 225

2xy = 112

Now consider ( x - y )² = x² + y² - 2xy

                     ( x - y )² = 113 - 112

                    ( x - y )² = 1

                      x - y = 1    ------------------ (4)

Now add ( 2 ) and ( 4 ) we get x = 8 and y = 7