If 6 ^ -1 (x^2-6 x+8.5 )= , then x is equal to - Vidyadip

Question

If $6 \sin ^{-1}\left(x^2-6 x+8.5\right)=\pi$, then $x$ is equal to

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Answer

$(b) :$ We have, $6 \sin ^{-1}\left(x^2-6 x+8.5\right)=\pi$
$\Rightarrow \sin ^{-1}\left(x^2-6 x+8.5\right)=\frac{\pi}{6}$
$\Rightarrow x^2-6 x+8.5=\sin \frac{\pi}{6}=\frac{1}{2}$
$\Rightarrow x^2-6 x+8=0$
$\Rightarrow(x-4)(x-2)=0$
$\Rightarrow x=4 \text { or } x=2$

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