Question

(ii) x²-8/x²=2 solve​

Answer 1

Question:

If x^2 - 8/x^2 = 2 , then solve for x.

Solution:

=> x^2 - 8/x^2 = 2

=> (x^4 - 8)/x^2 = 2

=> x^4 - 8 = 2x^2

=> x^4 - 2x^2 - 8 = 0

=> x^4 - 4x^2 + 2x^2 - 8 = 0

=> x^2(x^2 - 4) + 2(x^2 - 4) = 0

=> (x^2 - 4)(x^2 + 2) = 0

Case(1):

If x^2 - 4 = 0

=> x^2 = 4

=> x = ± √4

=> x = ± 2

Case (2):

If x^2 + 2 = 0

=> x^2 = -2

{This case will be rejected, because the square of any number is never negative}

Hence,

x = ± 2 are the solutions of the given equation.