Question

If X²+1/x²=7
Find the value of 3x²-3/x²

Answer 1

Answer: ±9√5

Step-by-step explanation:

$\tt Given: \\ \\ x^2 +\dfrac{1}{x^2} = 7  \\ \\ To\ Find: 3x^2 - \dfrac{3}{x^2} \\ \\ Adding\ 2 \ to\ both\ the\ side\ of\ the\ given\ equation\ : \\ \\ x^2 + \dfrac{1}{x^2}+2=9 \\ \\ \implies \Big(x + \dfrac{1}x\Big)^2 = 3^2 \\ \\ \implies \Big(x + \dfrac{1}x\Big) = \pm 3\\ \\ Similarly \ subtracting\ 2\ both\ sides\ we\ get: \\ \\ \Big(x - \dfrac{1}x\Big) = \pm \sqrt{5} \\ \\ \\ \Big(3x^2 - \dfrac{3}{x^2}\Big) = 3\Big(x + \dfrac{1}x\Big)\Big(x - \dfrac{1}x\Big) = \pm 9\sqrt{5}$

Answer 2

Step by step explanation:

${x}^{2} + \frac{1}{ {x}^{2} } = 7$

${(x + \frac{1}{x}) }^{2} - 2x \times \frac{1}{x} = 7$

${(x + \frac{1}{x} )}^{2} = 9$

$x + \frac{1}{x} = 3$

${(x - \frac{1}{x} )}^{2} + 2x \times \frac{1}{x} = 7$

${(x - \frac{1}{x} )}^{2} = 5$

$x - \frac{1}{x} = \sqrt{5}$

A/q,

$3 {x}^{2} - \frac{3}{ {x}^{2} }$

$3( {x}^{2} - \frac{1}{ {x}^{2} } )$

$3(x + \frac{1}{x} )(x - \frac{1}{x} )$

$3 \times 3 \times \sqrt{5} = 9 \sqrt{5}$

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