√x - (1/√x) = √2 - 1, where x ＞ 0, find the values of the following expressions and simplify the answers obtained.
(a) x + (1/x)
(b) x^2 + [1/(x^2)]
F.4 maths---10marks
2009-09-15 7:03 am
回答 (1)
2009-09-15 7:16 am
✔ 最佳答案
(a) x + (1/x)= [√x - (1/√x)]^2 + 2(√x )(1/√x)
= [√x - (1/√x)]^2 + 2
= (√2 - 1)^2 + 2
= (2 - 2√2 + 1) + 2
= 5 - 2√2
(b) x^2 + [1/(x^2)]
= [x + (1/x)]^2 - 2(x)(1/x)
= (5 - 2√2)^2 - 2
= (25 - 2(5)(2√2) + 8) - 2
= 31 - 20√2
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