If $x=2\sin\frac{3\pi}{10}$, find the value of the expression $$ W =2x^5+x^4-4x^3-4x^2-x+7 $$ After a bit of thought, I got : $$ x = \frac{\sqrt{5}+1}{2} $$ But I don't think my teacher expected me to substitute the value of $x$ into the expression. Is there anything I'm missing ?
2026-04-11 21:34:11.1775943251
If $x=2\sin\frac{3\pi}{10}$, find the value of the expression.
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Use $x^2-x-1=0$. It must help: $$2x^5+x^4-4x^3-4x^2+x+7=(x^2-x-1)(2x^3+3x^2+x)+7=7.$$