Question

find ; a^3+1/a^3, if a+1/a=5​

Answer 1

Step-by-step explanation:

$a + \frac{1}{a } = 5 \\ {a}^{3} + \frac{1}{ {a}^{a} } \\ = (a + \frac{1}{a} )( {a}^{2} - a \times \frac{1}{a} + \frac{1}{ {a}^{2} } ) \\ = (a + \frac{1}{a} )( {a}^{2} - 1 + \frac{1}{ {a}^{2} } ) \\ = 5 \times {(a + \frac{1}{a} )}^{2} - 2 - 1 \\ = 5 \times ({5}^{2} - 3) \\ = 5 \times (25 - 3) \\ = 5 \times 22 \\ = 110 \: \: ans$