Question

if x-1/x=4 find the value of x^2-1/x^2 and x^4-1/x^4

Answer 1

Answer:

$x - \frac{1}{x} = 4$

Squaring both sides, we get,

${x}^{2} + \frac{1}{ {x}^{2} } - 2.x. \frac{1}{x} = 16$

${x}^{2} + \frac{1}{ {x}^{2} } = 18$

Step-by-step explanation:

$(x + \frac{1}{x})^{2} = {x}^{2} + \frac{1}{x^{2} } + 2.x. \frac{1}{x}$

$= 20$

$x + \frac{1}{x} = \sqrt{20}$

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

$= 4 \sqrt{20}$

Similarly,

${x}^{4} - \frac{1}{ {x}^{4} } = ( {x}^{2} + \frac{1}{ {x}^{2} })( {x}^{2} - \frac{1}{ {x}^{2} })$

$= 72 \sqrt{20}$

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