Question

(x-1/x)=1 then find the value of (4x^2+4/x^2)

Answer 1

Answer:

$given \: that \\ x - \frac{1}{x} = 1 \\ on \: squaring \\ {(x - \frac{1}{x} ) }^{2} = {1}^{2} \\ {x}^{2} - 2 \times x \times \frac{1}{x} + \frac{1}{ {x}^{2} } = 1 \\ {x}^{2} - 2 + \frac{1}{ {x}^{2} } = 1 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 1 +2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 3 \\ mutiplying \: both \: sides \: by \: 4 \\ 4( {x}^{2} + \frac{1}{ {x}^{2} } ) = 3 \times {4} \\ 4 {x}^{2} + \frac{4}{ {x}^{2} } = 12 \\ your \: answer \: is \: 12$

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