Question

If x=2+^3 ,findx^3+1/x^3​

Answer 1

Answer:

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Step-by-step explanation:

HERE....

$x = 2+ \sqrt{3}$

$\frac{1}{x} = \frac{1}{2 + \sqrt{3} }$

RATIONALIZE THE DENOMINATOR

$\frac{1}{x} = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} }$

$\frac{1}{x} = \frac{2 - \sqrt{3} }{4 - 3}$

$\frac{1}{x} = \frac{2 - \sqrt{3} }{1}$

NOW ... COMING BACK TO THE PROVE

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

$= {(2 + \sqrt{3}) }^{2} + {(2 - \sqrt{3} )}^{2} \\ = (4 + 3 + 4\sqrt{3} ) +( 4 + 3 - 4\sqrt{3} ) \\ = 7 + 4\sqrt{3} + 7 - 4\sqrt{3} \\ = 7 + 7 \\ = 14$

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UR ANSWER IS .....14

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Answer 2

Answer:

14

Step-by-step explanation: