Question

if x-1/x =6,then find the value of x²-1/x²​

Answer 1

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Answer 2

$\bold\pink{cube \: both \: sides \: of \: the \: given \: equation}$

$\bold{( - \frac{1}{x} ) {}^{3} = {6}^{3}}$

$\bold{{ x}^{3} - \frac{1}{ {x}^{3} } - 3 \times x \times \frac{1}{x} (x - \frac{1}{x} ) = 216}$

$\bold {{x}^{3} - \frac{1}{ {x}^{3} } - 18 = 216}$

$\bold{{x}^{3} - \frac{1}{{x}^{3} } = 234}$

$\bold\orange{square \: both \: sides \: of \: the \: given \: equation}$

$(x - \frac{1}{x} ^{2} = {6}^{2}$

${x}^{2} + \frac{1}{ {x}^{2}} - 2 \times x \times \frac{1}{x} = 36$

${x}^{2} + \frac{1}{ {x}^{2} } - 2 = 36$

${x}^{2} + \frac{1}{ {x}^{2} } = 38$