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