If x=1+√2, evaluate x³+1/x³.

Mathematics

1 answer:

aleksandr82 [10.1K]3 years ago

3 0

Answer:

10√2

Step-by-step explanation:

If x=1+√2, evaluate x³+1/x³

--------

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

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