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Question 6

If $$(x+1)^2 = x$$, the value of $$11x^3 + 8x^2 + 8x - 2$$ is

Solution

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Expanding gives $$x^2+x+1=0$$, so $$x^2=-x-1$$. Then $$x^3=x\cdot x^2=x(-x-1)=-x^2-x=(x+1)-x=1$$. Substituting, $$11x^3+8x^2+8x-2=11(1)+8(-x-1)+8x-2=11-8x-8+8x-2=1$$.

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