Question

If x+y=3^1/2 x-y= 2^1/2

Then the expression 8xy(x² + y²) has the value ?

Answer 1

Given x+y =3^1/2 It means (x+y)² = 3

Given x-y =2^1/2 It means (x-y)² = 2

(x+y)² = x²+y²+2xy

(x-y)² = x²+y²-2xy

(x+y)²-(x-y)² = 4xy

3-2 = 4xy

1 = 4xy

xy = 1/4

(x+y)² = x²+y²+2xy

It means x²+y² = (x+y)²-2xy

So x²+y² = 3-2*(1/4)= 3-1/2 = 5/2

x²+y² = 5/2

8xy(x² + y²) = 8*(1/4)*(5/2) = 5

Answer : 5