Question

If x-y = 10 and xy=16 find the value of x^2 + y^2

Answer 1

hey dear here is ur answer..........

x + y = 10

Solve for y the first equation.

y = 10 - x

Now use the second equation

xy = 16

Substitute y from the first equation into he second

x*(10 -x) = 16

10x -x^2 = 16

Now solve for x:

x^2 - 10x + 16 = 0.

(x - 8)(x - 2)= 0

x = 8 or x = 2

For x = 8:

x^2 + xy + y^2 =

8^2 + 8(10–8) +(10 - 8)^2 =

64 + 16 + 4 = 84

For x = 2:

x^2 + xy + y^2 =

2^2 + 2(10 - 2) + (10– 2)^2 =

4 + 16 + 64 = 84

x^2 +xy + y^2 = 84

Answer 2

(x-y)^2=x^2-2xy+y^2

100=x^2+y^2-32

x^2+y^2=132