Question

if x-1_x=√3,then find the value of x^3-1_x^3​

Answer 1

Answer:

6√3

Step-by-step explanation:

$given \\ \: \: \: \: \: x - \frac{1}{x} = \sqrt{3} \\ now \\ \: \: \: \: {x}^{3} - \frac{1}{x^{3} } = t ^{3 } + 3t(where \: \: \: \: t = (x - \frac{1}{x} )) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = { (\sqrt{3}) }^{3 } + 3 \times \sqrt{3} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3 \sqrt{3} + 3 \sqrt{3} = 6 \sqrt{3} \\ ansssssssssssssss$

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