If a- 1-a-4 and q-0- then a 3-1- a 3 is equal toA- 72B- 56C- 76D- 91

The correct option is C 76Given that a 1/a=4 (a 1/a)^3 = (a)^3 (1/a)^3 3× a×1/a(a 1/a) (a)^3 (1/a)^3 = (a 1/a)^3 + 3(a 1/a) (a)^3 (1/a)^3 = 64+12 . ...

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Byju's Answer

Standard VIII

Mathematics

Expansion of (a-b)^3

If a- 1/a=4 a...

Question

If a- $\frac{1}{a}$ = 4 and $a \neq 0$ ; then $a^{3} - \frac{1}{a^{3}}$ is equal to

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Solution

The correct option is C 76
Given that $a - \frac{1}{a} = 4$

$(a - \frac{1}{a})^{3} = (a)^{3} - (\frac{1}{a})^{3} - 3 \times a \times \frac{1}{a} (a - \frac{1}{a})$

$(a)^{3} - (\frac{1}{a})^{3} = (a - \frac{1}{a})^{3} + 3 (a - \frac{1}{a})$

$(a)^{3} - (\frac{1}{a})^{3} = 64 + 12$ ......[ since $a - \frac{1}{a} = 4$ ]

$(a)^{3} - (\frac{1}{a})^{3} = 76$

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If a-1a= 4 and a≠0; then a3−1a3 is equal to

The correct option is C 76Given that a−1a=4 (a−1a)3=(a)3−(1a)3−3×a×1a(a−1a) (a)3−(1a)3=(a−1a)3+3(a−1a) (a)3−(1a)3=64+12 ......[ since a−1a=4] (a)3−(1a)3=76

If a- $\frac{1}{a}$ = 4 and $a \neq 0$ ; then $a^{3} - \frac{1}{a^{3}}$ is equal to