If x^{2}-x+1=0 then what is (x-\frac{1}{x})^{2}+(x-\frac{1}{x})^{4}+(x-\frac{1}{x})^{8} equal to?

Explanation

x^2-x+1=0 \implies x+1/x=1. Then (x-1/x)^2 = (x+1/x)^2 - 4 = 1 - 4 = -3. The required expression is (-3) + (-3)^2 + (-3)^4 = -3 + 9 + 81 = 87.

Related questions on Algebra

• How many four-digit natural numbers are there such that <strong>ALL</strong> of the digits are odd?
• What is \sum_{r=0}^{n}2^{r}C(n,r) equal to ?
• If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) a...
• Consider the following statements : 1. If f is the subset of Z\times Z defined by f=\{(xy,x-y);x,y\in Z\}, then f is a function from...
• For how many quadratic equations, the sum of roots is equal to the product of roots?