Question

If under root X minus 1 by under root X is = 3 ,then find the value of X cube + 1 by X cube

Answer 1

Answer :

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

On squaring both sides ;

$\sf ( \sqrt{x} ) {}^{2} + ( \frac{1}{ \sqrt{x} } ) {}^{2} = (3) {}^{2} \\ \\ \sf x + \frac{1}{x} + 2 = 9 \\ \\ \sf x + \frac{1}{x} = 9 - 3 \\ \\ \sf x + \frac{1}{x} = 6$

On cubing both sides ;

$\sf (x + \frac{1}{x} ) {}^{3} = (6) {}^{3} \\ \\ \sf x {}^{3} + \frac{1}{x {}^{3} } + 3(x + \frac{1}{x} ) = 216 \\ \\ \sf x {}^{3} + \frac{1}{x {}^{3} } + 3 \times 6 = 216 \\ \\ \sf x {}^{3} + \frac{1}{x {}^{3} } + 18 = 216 \\ \\ \sf x {}^{3} + \frac{1}{x {}^{3} } = 216 - 18 \\ \\ \bf x {}^{3} + \frac{1}{x {}^{3} } = 198$

Hence, the answer is 198.

Answer 2

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her is your answer
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