alpha, beta ,gamma are roots of eq | vedclass

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Question

$x+\beta+\gamma=0$

$	herefore \alpha+\beta=-\gamma, \beta+\gamma=-\alpha, \gamma+\alpha=-\beta$

$	herefore$ Roots of Reqd. equation are $\frac

Vedclass · Accepted Answer

$x^3 -x^2 + 1 = 0$

Vedclass · Answer

$x+\beta+\gamma=0$

$	herefore \alpha+\beta=-\gamma, \beta+\gamma=-\alpha, \gamma+\alpha=-\beta$

$	herefore$ Roots of Reqd. equation are $\frac{-1}{\alpha}, \frac{-1}{\beta}, \frac{-1}{\gamma}$

-ve recipical roots,

$	herefore 	ext { Replace } \mathrm{x} ightarrow \frac{-1}{\mathrm{x}}$

$\frac{-1}{x^{3}}+\frac{1}{x}-1=0 \quad \Rightarrow-1+x^{2}-x^{3}=0$

$	ext { or } x^{3}-x^{2}+1=0$

$\alpha$, $\beta$ ,$\gamma$ are roots of equatiuon $x^3 -x -1 = 0$ then equation whose roots are $\frac{1}{{\beta + \gamma }},\frac{1}{{\gamma + \alpha }},\frac{1}{{\alpha + \beta }}$ is

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