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Question
Expand.
`(x + 1/x)^3`
Sum
Solution
Here, a = x, b = `1/x`
We know that,
(a + b)3 = a3 + 3a2b + 3ab2 + b3
∴ `(x + 1/x)^3 = x^3 + 3(x)^2(1/x) + 3(x)(1/x)^2 + (1/x)^3`
= `x^3 + 3x^2 xx 1/x + 3x xx 1/x^2 + 1/x^3`
= `x^3 + 3x + 3/x + 1/x^3`
∴ `(x + 1/x)^3 = x^3 + 3x + 3/x + 1/x^3`
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