Question

if x-y=6 and xy=8 , find the value of x2 + y2​

Answer 1

Answer:

given that

x-y=6,xy=8

y=8/x equation 1

x/1-8/x=6

x^2-8/x=6

x^2-8=6x

x^2-6x-8=0 (it is a quadratic equation)

x^2-2x-4x-(2*4)=0

x(x-2) +4(x-2)

(x-2) (x+4)=0

x-2=0 or x+4=0

x=2 or x=-4

then x =2 equation 2

equation 2 in 1

x-y=6

2-y=6

2=6+y

y=2-6

y=-4

then x^2+y^2

(2)^2+(-4)^2

4+16=20

Answer 2

x - y = 6

( x - y )² = ( 6 ) ²

x² - 2xy + y² = 36

( x² + y²) - 2xy = 36

( x² + y²) -2(8)=36

( x² + y²)-16= 36

x² + y² = 36+16

x²+y² = 52