Question

If x=1+√2, evaluate x³+1/x³.

Answer 1

10√2

Explanation:

If x=1+√2, evaluate x³+1/x³

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• x³+1/x³= (x+1/x)(x²-x*1/x+1/x²)=(x+1/x)(x²+1/x²+2-3)= (x+1/x)((x+1/x)²-3)
• x+1/x= 1+√2 + 1/(1+√2)= 1+√2+(1-√2)/(1-√2)(1+√2)= 1+√2 - (1-√2)= 2√2
• x³+1/x³= 2√2((2√2)²-3)= 2√2(8-3)= 10√2