Question

If x = 1 - √2, find the value of (x – 1/x)cube.

Answer 1

Step-by-step explanation:

x = (1 - √2)

1/x = 1/(1 - √2)

=> 1/x = 1(1 + √2)/(1 - √2)(1 + √2)

multiplying nr and dr by conjugate of 1 - √2

=> 1/x = (1 + √2)/-1

=> 1/x = -1 - √2

now x - 1/x = 1 - √2 - (-1 - √2)

=> 1 - √2 + 1 + √2

=> 2

therefore (x - 1/x)³ = 2³ => 8