It is given that {x + [1 / (x^2)}^5 - { x- [1 / (x^2)] }^5 = a(x^2) + b/(x^4) + c/(x^10)
(a) Find the values of a, b and c.
(b) Hence evaluate [√2 + (1/2)]^5 - [√2 - (1/2)]^5
binomial theorem-3-
2009-10-26 11:18 pm
回答 (1)
2009-10-27 4:45 am
✔ 最佳答案
(a) {x + [1 / (x^2)]}^5 - { x- [1 / (x^2)] }^5= x^5 + 5(x^4)(1/x^2) + 10(x^3)(1/x^4) + 10(x^2)(1/x^6) + 5(x)(1/x^8) + 1/x^10 - [x^5 - 5(x^4)(1/x^2) + 10(x^3)(1/x^4) - 10(x^2)(1/x^6) + 5(x)(1/x^8) - 1/x^10]
= 10x^2 + 20/x^4 + 2/x^10
So a = 10, b = 20, c = 2
(b) Put x = √2, [√2 + (1/2)]^5 - [√2 - (1/2)]^5
= 10(2) + 20/(4) + 2/(32)
= 20 + 5 + 0.0625
= 25.0625
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