JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
The product of all solutions of the equation \(\mathrm{e}^{5\left(\log _{\mathrm{e}} x\right)^2+3}=x^8, x\gt0\), is :
- A \(e^{8 / 5}\)
- B \(e^{6 / 5}\)
- C \(\mathrm{e}^2\)
- D e
Answer & Solution
Correct Answer
(A) \(e^{8 / 5}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \mathrm{e}^{5(\ln x)^2+3}=\mathrm{x}^8 \\ & \Rightarrow \ell \mathrm{ne}^{5(\ln x)^2+3}=\ell \mathrm{nn}^8 \\ & \Rightarrow 5(\ln \mathrm{x})^2+3=8 \ell \mathrm{nx} \\ & (\ell \mathrm{nx}=\mathrm{t}) \\ & \Rightarrow 5 \mathrm{t}^2-8 \mathrm{t}+3=0 \\ & \quad…
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