Question

find: a³-1/a³ , if a-1/a= 4​

Answer 1

Answer:

76

$a - \frac{1}{a} = 4 \\ \\ a {}^{3} - \frac{1}{ {a}^{3} } = (a - \frac{1}{a} )((a {}^{2} ) + (\frac{1}{a} ) {}^{2} + a \times \frac{1}{a} ) \\ a {}^{3} - \frac{1}{ {a}^{3} } = 4 \times ( {a}^{2} + \frac{1}{ {a}^{2} } + 1) \\ a {}^{3} - \frac{1}{ {a}^{3} } = 4 \times ( {a}^{2} + \frac{1}{ {a}^{2} } + 1 - 2 + 2) \\ a {}^{3} - \frac{1}{ {a}^{3} } = 4 \times ( ({a}^{2} + \frac{1}{ {a}^{2} } - 2) + 3) \\ a {}^{3} - \frac{1}{ {a}^{3} } = 4 \times ( ( a - \frac{1}{a}) {}^{2} + 3) \\ a {}^{3} - \frac{1}{ {a}^{3} } = 4 \times (4 {}^{2} + 3) \\ = 4 \times 19 = 76$

Answer 2

Step-by-step explanation:

a-1/a=4

Square on both sides

(a-1/a)²=4²

a²+1/a²-2a./a=16

a²+1/a²-2=16

Aa²+1/a²=14

a³-b³=(a-b) (a²+b²+ab)

Using this formula we get

a³-1/a³=(a-1/a) (a²+1/a²+a. 1/a)

=4 (14+1)

=4*15=60