Question

If a is not equal to 0
And
a-1/a=4;
Find
a^3-1/a^3

Answer 1

Answer:

$\sf a - \frac{1}{a} = 4 \\ \\ \bf on \: cubing \: both \: sides : \\ \\ \sf( a - \frac{1}{a} ) {}^{3} = (4){}^{3} \\ \\ \sf a{}^{3} - \frac{1}{a {}^{3}} - 3(a - \frac{1}{a} ) = 64 \\ \\ \sf a{}^{3} - \frac{1}{a{}^{3}} - 3 \times 4 = 64 \\ \\ \sf a{}^{3} - \frac{1}{a{}^{3}} - 12 = 64 \\ \\ \sf a{}^{3} - \frac{1}{a{}^{3}} = 64 + 12 \\ \\ \boxed{ \bf a{}^{3} - \frac{1}{a{}^{3}} = 76}$

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