The number of distinct real roots of the equa | vedclass

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Question

$x^{7}-7 x-2=0$

$x^{7}-7 x=2$

$f(x)=x^{7}-7 x 	ext { (odd)  } and \,y=2$

$f(x)=x\left(x^{2}-7^{1 / 3}ight)\left(x^{4}+x^{2} \cdot 7^{

Vedclass · Accepted Answer

$3$

Vedclass · Answer

$x^{7}-7 x-2=0$

$x^{7}-7 x=2$

$f(x)=x^{7}-7 x 	ext { (odd)  } and \,y=2$

$f(x)=x\left(x^{2}-7^{1 / 3}ight)\left(x^{4}+x^{2} \cdot 7^{1 / 3}+7^{2 / 3}ight)$

$f^{\prime}(x)=7\left(x^{6}-1ight)=7\left(x^{2}-1ight)\left(x^{4}+x^{2}+1ight)$

$f^{\prime}(x)=0 \Rightarrow x=\pm 1$

$f(x)=2$ has $3$ real distinct solution

The number of distinct real roots of the equation $x ^{7}-7 x -2=0$ is

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