2021-11-30

Dare2Solve | Algebraic equation on fifth power

This question was uploaded on 29/11/21 on social media accounts.

Solution:

From the first equation:
\[x^3 = 2-x\]
\[\Rightarrow x^5 = 2x^2 - x^3\]
\[\Rightarrow x^4 = 2x - x^2\]
Now put these values in the given equation:
\[2x^2 - x^3 + 2x - x^2 + 4(2-x) - x^2 + x + 7\]
\[= - x^3 + 8 -x + 7\]
\[= x - 2 + 8 -x + 7\]
\[= 13\]
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