(7 ((6x−10))^(1/5) )^2 = ((49)/( ((1/x^2 ))^(1/5) ))


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Question Number 157441 by bobhans last updated on 23/Oct/21

${(7 \sqrt[5]{6 x - 10})}^{2} = \frac{49}{\sqrt[5]{\frac{1}{x^{2}}}}$
	Answered by MJS_new last updated on 23/Oct/21

	$49 {(6 x - 10)}^{2 / 5} = 49 x^{2 / 5}$ ${(6 x - 10)}^{2} = x^{2}$ $x^{2} - \frac{24}{7} x + \frac{20}{7} = 0$ $x = \frac{10}{7} \lor x = 2$
	Answered by cortano last updated on 23/Oct/21

	$\Rightarrow 49 \sqrt[5]{{(\frac{6 x - 10}{x})}^{2}} = 49$ $\Rightarrow {(\frac{6 x - 10}{x})}^{2} = 1$ $\Rightarrow {(6 x - 10)}^{2} - x^{2} = 0$ $\Rightarrow (7 x - 10) (5 x - 10) = 0$ $\Rightarrow x_{1} = \frac{10}{7} \land x_{2} = 2$
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