Question

If
$2x - \frac{1}{x } = 4$
So, What is
${x}^{2} + \frac{1}{4x {}^{2} }$
??​

Answer 1

EXPLANATION :

Given :

$\bull \: \: \: \: \: \: \: \: \bf \underline{ 2x - \frac{1}{x} = 4}$

Solution :

$\sf \: \: {(2x - \frac{1}{x}) }^{2} = {4}^{2} \\ \\ \sf\implies \: 4 {x}^{2} + \frac{1}{ {x}^{2} } - 2 \times 2x \times \frac{1}{x} = 4 \\ \\ \sf \implies4 {x}^{2} + \frac{1}{ {x}^{2} } - 4 = 4 \\ \\ \implies \sf4 {x}^{2} + \frac{1}{ {x}^{2} } = 8 \\ \\ \sf \implies \frac{1}{4} (4 {x}^{2} + \frac{1}{ {x}^{2} } ) = 8 \times \frac{1}{4} \\ \\ \sf \: \implies\boxed{ \boxed{ \mathfrak{{x}^{2} + \frac{1}{4 {x}^{2} } = 4}}}$

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HOPE THIS IS HELPFUL...

Answer 2

hiiu

have a nice day

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