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Kinetic Friction

5 x+2 2+5 x-2...

Question

$\frac{(5 x + 2)^{2} + (5 x - 2)^{2}}{(5 x + 2)^{2} - (5 x - 2)^{2}} = \frac{13}{12}$

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Solution

$\frac{{(5 x + 2)}^{2} + {(5 x - 2)}^{2}}{{(5 x + 2)}^{2} - {(5 x - 2)}^{2}} = \frac{13}{12} \Rightarrow \frac{{(5 x + 2)}^{2} + {(5 x - 2)}^{2} + {(5 x + 2)}^{2} - {(5 x - 2)}^{2}}{{(5 x + 2)}^{2} + {(5 x - 2)}^{2} - {(5 x + 2)}^{2} - {(5 x - 2)}^{2}} = \frac{13 + 12}{13 - 12} (Componendo and dividendo)$
$\Rightarrow \frac{2 {(5 x + 2)}^{2}}{2 {(5 x - 2)}^{2}} = \frac{25}{1}$
$Taking square roots, we get :$

$\frac{5 x + 2}{5 x - 2} = \frac{5}{1} or \frac{5 x + 2}{5 x - 2} = \frac{- 5}{1}$
$\Rightarrow 5 x + 2 = 5 (5 x - 2) or 5 x + 2 = - 5 (5 x - 2)$
$\Rightarrow 5 x + 2 = 25 x - 10 or 5 x + 2 = - 25 x + 10$
$\Rightarrow - 20 x = - 12 or 30 x = 8$
$\Rightarrow x = \frac{3}{5} or x = \frac{4}{15}$

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\frac{(5 x + 2)^{2} - (5 x - 2)^{2}}{(5 x + 2)^{2} + (5 x - 2)^{2}} = \frac{12}{13}

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