Question

If x=3+√8, then find the value ofx^3+1/x^3.

Answer 1

Answer:

Answer is 198.

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Step-by-step explanation:

Given,

$x = 3 + \sqrt{8} \\ \therefore \: \frac{1}{x} = \frac{1}{3 + \sqrt{8} } \\ = > \frac{1}{x} = \frac{3 - \sqrt{8} }{(3 + \sqrt{8} )(3 - \sqrt{8} )} \\ = > \frac{1}{x} = \frac{3 - \sqrt{8} }{( {3})^{2} - { (\sqrt{8} )}^{2} } \\ = > \frac{1}{x} = \frac{3 - \sqrt{8} }{9 - 8} \\ = > \frac{1}{x} = 3 - \sqrt{8} \\ \therefore \: {x}^{3} + \frac{1}{ {x}^{3} } = {(x + \frac{1}{x}) }^{3} - 3.x. \frac{1}{x} (x + \frac{1}{x} ) \\ = > {x}^{3} + \frac{1}{ {x}^{3} } = {(3 + \sqrt{8} + 3 - \sqrt{8} ) }^{3} - 3(3 + \sqrt{8} + 3 - \sqrt{8} ) \\ = > {x}^{3} + \frac{1}{ {x}^{3} } = {6}^{3} - 3 \times 6 \\ = > {x}^{3} + \frac{1}{ {x}^{3} } = 216 - 18 \\ = > {x}^{3} + \frac{1}{ {x}^{3} } = 198$