Question

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Answer 1

Answer:

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Answer 2

Answer:

x = √2 + 1

Then, 1/x = 1/√2 + 1

Rationalizing 1/√2 + 1

= 1 (√2 - 1) / (√2 + 1) (√2 - 1)

= √2 - 1 / (√2)^2 - (1)^2

= √2 - 1 / 2-1

= √2 - 1 / 1

= √2 - 1

Thus, 1/x = √2 - 1

x + 1/x = √2 + 1 + √2 - 1( +1 and -1 will get cancelled)

x + 1/x = √2 + √2

x + 1/x = 2√2

Find x^2 + 1/x^2.

x + 1/x = 2√2

(x + 1/x)^2 = (2√2)^2

=> x^2 + 1/x^2 + 2 = 8

=> x^2 + 1/x^2 = 8-2

=> x^2 + 1/x^2 = 6

Thus, x^2 + 1/x^2 is 6.

(x^2 means x to the power 2)

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