If 203-2x2=4053x2-2, then x=

Given 20 (3−2x2)= (405) 3x2−2⇒ 20 3−2x2=(40×40×5) 3x2−2⇒ 203−2x2= (20)32 (3x2−2)∴ 3−2x2=32(3x2−2)⇒ 6−4x2=9x2−6⇒ 13x2=12⇒ x2= 1213⇒ x= ± 1213

If 203-2x2=4053x2-2, then x=

Given 20 (3−2x2)= (405) 3x2−2⇒ 20 3−2x2=(40×40×5) 3x2−2⇒ 203−2x2= (20)32 (3x2−2)∴ 3−2x2=32(3x2−2)⇒ 6−4x2=9x2−6⇒ 13x2=12⇒ x2= 1213⇒ x= ± 1213

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If $20^{3 - 2 x^{2}} = {(40 \sqrt{5})}^{3 x^{2} - 2},$ then $x =$

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$\pm \sqrt{12 / 13}$

$\pm \sqrt{4 / 5}$

$\pm \sqrt{13 / 12}$

$\pm \sqrt{5 / 4}$

answer is B.

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Detailed Solution

$\begin{array}{l} G i v e n 20^{(3 - 2 x^{2})} = {(40 \sqrt{5})}^{3 x^{2} - 2} \\ \Rightarrow 20^{3 - 2 x^{2}} = (\sqrt{40 \times 40 \times 5})^{3 x^{2} - 2} \\ \Rightarrow 20^{3 - 2 x^{2}} = {(20)}^{\frac{3}{2} (3 x^{2} - 2)} \\ ∴ 3 - 2 x^{2} = \frac{3}{2} (3 x^{2} - 2) \\ \Rightarrow 6 - 4 x^{2} = 9 x^{2} - 6 \\ \Rightarrow 13 x^{2} = 12 \\ \Rightarrow x^{2} = \frac{12}{13} \\ \Rightarrow x = \pm \sqrt{\frac{12}{13}} \end{array}$