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Expansion of (a ± b)³

if (x+1/x) = ...

Question

if (x+1/x) = 4 find the value of x cube +1/ x cube

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Solution

x + 1/x = 4

(x + 1/x)³ = 4³

x³ + 1/x³+ 3 x Ã— 1/ x Ã— (x + 1/x) = 64

x³+ 1/x³+ 3 Ã— 4 = 64 [Because x + 1/x = 4]

x³+ 1/x³+ 12 = 64

x³+ 1/x³= 64 - 12

= 52

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