Question

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

• A. $1$
• B. $2$
• C. $3$
• D. $8$

Answer 1

Answer: (B)

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