Solve: If x = 1 – √2, find 1/x, (x – 1/x)4:

Solve: If x = 1 – √2, find 1/x, (x – 1/x)⁴

Solution:

Given:

x = 1 – √2

so,

1/x = 1/(1 – √2)

By rationalizing the denominator,

1/ (1 – √2) = [1(1 + √2)] / [(1 – √2) (1 + √2)]

= [(1 + √2)] / [1² – (√2)²]

= [(1 + √2)] / [1 – 2]

= (1 + √2) / -1

= -(1 + √2 )

Then,

(x – 1/x)⁴ = [1 – √2 – (-1 – √2)]⁴

= [1 – √2 + 1 + √2]⁴

= 2⁴

= 16

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