Question

if x^2 + 1/x^2 = 6 find x^3 - 1/x^3

Answer 1

Step-by-step explanation:

Given:-

x²+1/x²=6. (1)

Find:-

x³-1/x³=?

solution:-

x²+1/x²-2=6-2

(x)²+(1/x)²-2(x)(1/x)=4

(x-1/x)²=(2)²

x-1/x=2. (2)

taking cube on both sides of (2)

x³-1/x³-3x²(1/x)+3x(1/x)²=8

x³-1/x³-3(x-1/x)=8

x³-1/x³-3(2)=8

x³-1/x³=14

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