Question

10. If x = (a+1/a) and y = (a -. 1/a) then let's find the value of x4+y4-2x2y2
​

Answer 1

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

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