Question

2. If x = (a+1÷a) and y = (a-1÷a) then let's find the value of x^4+y^4-2x^2y
^2
2

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Answer 1

Step-by-step explanation:

The value of  = 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

= 16

Above equation is the required equation, therefore

The value of the expression is 16.