Question

if x-1/x= 1/2, find the value of 4x^{2} + 4/x^{2}

Answer 1

$Answer \: \\ \\ x - \frac{1}{x} = \frac{1}{2} \: \:(Given) \: \: \: \: \: find \: \: \: 4x {}^{2} + \frac{4}{x {}^{2} } \\ \\ x - \frac{1}{x} = \frac{1}{2} \\ \\ Squaring \: \: on \: both \: sides \: we \: have \\ \\ (x - \frac{1}{x} ) {}^{2} = ( \frac{1}{2} ) {}^{2} \\ \\ x {}^{2} + \frac{1}{x {}^{2} } - 2 (\frac{x}{x} ) = \frac{1}{4} \\ \\ x {}^{2} + \frac{1}{x {}^{2} } = \frac{1}{4} + 2 \\ \\ x {}^{2} + \frac{1}{x {}^{2} } = \frac{8 + 1}{4} \\ \\ x {}^{2} + \frac{1}{x {}^{2} } = \frac{9}{4} \\ \\ Multiply \: both \: sides \: by \: 4 \: we \: have \\ \\ 4x {}^{2} + \frac{4}{x {}^{2} } = \frac{9 \times 4}{4} \\ \\ 4x {}^{2} + \frac{4}{x {}^{2} } = 9 \\ \\ NOTE \: \\ \\ (x - y) {}^{2} = x {}^{2} + y {}^{2} - 2xy$

Answer 2

Step-by-step explanation:

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