Question

If $2^{\left(\log _2 x\right)^2}+x^{\log _2 x}=32$, then

• A. equation has two rational solutions.
• B. equation has one rational and one irrational solutions.
• C. product of all solutions is 1 .
• D. product of all solutions is $2 \sqrt{2}$.

Answer 1

Answer: (A), (C)

Put $\log _2 x=y \Rightarrow x=2^y \Rightarrow 2^{y^2}+2^{y^2}=32$
$\Rightarrow y = \pm 2$. So, $x =4, \frac{1}{4}$