Question

Find the value of x^2+y^2 and xy when x+y=8 , x-y=3

Answer 1

x + y = 8 => y = 8 - x ....(i)
Then, x - y = 3 => x - ( 8 - x ) = 3 (from (i))
=> x - 8 + x = 3 = 2x = 3+8 = 11 => x = 11/2
y = 8 - 11/2 = (16-11)/2 = 5/2
=> x² + y² = (11/2)²+(5/2)² = 121/4 + 25/4 = 174/4 = 43.5