Question

If x= a+1/a and y= a-1/a than find the value of x^4+y^4-2x^2y^2

Answer 1

x+y=2a
x-y=2/a
(x+y)(x-y)=4
x^2 - y^2=4
Squareing both sides we get
x^4+y^4-2x^2 y^2 =16

Answer 2

The value of $x^4+y^4-2x^2y^2$ = 16.

• Given :

x = a + 1/a   (Equation 1)

y = a - 1/a     (Equation 2)

• Adding both the equations , we get

x + y = 2a         (Equation 3)

• Subtracting equation 2 from equation 1

x - y = 2/a          (Equation 4)

• Now multiplying equation 3 and 4

(x + y)(x - y) = (2a)(2/a)

x²-y² = 4

• Now squaring both sides we get,

(x²-y²)² = 4²

$x^4-2x^2y^2+y^4$ = 16

Above equation is the required equation, therefore

• The value of the expression is 16.