AP EAMCET · Maths · Basic of Mathematics
If \(12^{4+2 x^2}=(24 \sqrt{3})^{3 x^2-2}\), then \(x\) is equal to
- A \(\pm \sqrt{\frac{13}{12}}\)
- B \(\pm \sqrt{\frac{14}{5}}\)
- C \(\pm \sqrt{\frac{12}{13}}\)
- D \(\pm \sqrt{\frac{5}{14}}\)
Answer & Solution
Correct Answer
(B) \(\pm \sqrt{\frac{14}{5}}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { We have, }(12)^{4-2 x^2}=(24 \sqrt{3})^{3 x^2-2} \\ & \begin{array}{l}(12)^{4+2 x^2}=(12)^{\frac{3}{2}}\left(3 x^2-2\right)\end{array} \\ & 4+2 x^2=\frac{3}{2}\left(3 x^2-2\right) \\ & 8+4 x^2=9 x^2-6 \\ & 9 x^2-4 x^2=8+6 \\ & \Rightarrow 5 x^2=14 \quad…
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