If $\mathrm{a}$ and $\mathrm{b}$ are the roots of the equation $\mathrm{y}^2+\mathrm{y}+1=0$, then the value of $a^4+b^4+a^{-1} b^{-1}$ is

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Aicharya · Accepted Answer

Given the equation $y^2+y+1=0$ $\begin{aligned} & 	ext { Now, } a^4+b^4+a^{-1} b^{-1}=a^4+b^4+\frac{1}{a b} \ & =\left(a^2+b^2ight)^2-2 a^2 b^2+\frac{1}{1} \ & =\left((a+b)^2-2 a bight)^2-2 	imes 1+1 \ & =\left((-1)^2-2ight)^2-1=1-1=0 \end{aligned}$

If $\mathrm{a}$ and $\mathrm{b}$ are the roots of the equation $\mathrm{y}^2+\mathrm{y}+1=0$, then the value…

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