Question

is x/y=a+1/a-1 then find the value of x2-y2/x2+y2​

Answer 1

Answer:

The value of x^4+y^4-2x^2y^2x

4

+y

4

−2x

2

y

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^4x

4

−2x

2

y

2

+y

4

= 16

Above equation is the required equation, therefore

The value of the expression is 16.