Question

Consider the equation $\sin ^{-1}\left(x^2-6 x+\frac{17}{2}\right)+\cos ^{-1} k=\frac{\pi}{2}$, then

• A. the largest value of $k$ for which the equation has 2 distinct solution is 1 .
• B. the equation must have real root if $k \in\left(\frac{-1}{2}, 1\right)$.
• C. the equation must have real root if $k \in\left(-1, \frac{-1}{2}\right)$.
• D. the equation has unique solution if $k=\frac{-1}{2}$.

Answer 1

Answer: (A), (B), (D)

For the solution of equation, we must have $\left(x^2-6 x+\frac{17}{2}\right)=k$, where $k \in[-1,1]$ and $\left( x ^2-6 x +\frac{17}{2}\right) \in[-1,1]$