Question

Search Results Web results if a-1/a=3; find a3-1/a3

Answer 1

$Given \: a - \frac{1}{a} = 3 \: --(1)$

/* By Algebraic Identity */

$\boxed {\pink { x^{3}-y^{3} = (x-y)^{3} - 3xy(x-y) }}$

$\red{ Value \:of \: a^{3} - \frac{1}{a^{3}} } \\= \Big( a - \frac{1}{a}\Big)^{3} - 3 \times a \times \frac{1}{a} \Big( a - \frac{1}{a}\Big) \\= 3^{3} - 3\times 3 \\ = 27 - 9 \\= 18$

Therefore.,

$\red{ Value \:of \: a^{3} - \frac{1}{a^{3}} }\green {= 18}$

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