1 MC Question about numbers and functions

2008-08-04 7:19 pm

If x + 1/x = 1 + √2, then x^2 + 1/x^2 =

A.1+√2
B. 6
C. 7/3
D. 1+2√2

Please answer the above question with explanation and steps, thanks!

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回答 (1)

2008-08-04 7:31 pm

✔ 最佳答案

(x + 1/x)^2 = x^2 + 2 + (1/x)^2 . Therefore,
x^2 + (1/x)^2 = (x + 1/x)^2 - 2 = (1+sqrt2)^2 - 2 = 1 + 2 + 2sqrt2 -2 = 1 + 2sqrt2.
So the answer is D.

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