Question

if a+1/a=5 then prove that a³+1/a³= 110​

Answer 1

Answer:

$a + \frac{1}{a} = 5 \\ = > \bf{cubing \: both \: sides} \\ = > (a + \frac{1}{a} {)}^{3} = {5}^{3} \\ = > \color{purple}{( {x}^{} + {y}^{} {)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y) } \\ = > {a}^{3} + \frac{1}{ {a}^{3} } + (3 \times a \times \frac{1}{a} ) \times (a + \frac{1}{a} ) = 125 \\ = > {a}^{3} + \frac{1}{ {a}^{3} } + 3 \times 5 = 125 \: \: \: \ \: \: \: \: (a + \frac{1}{a} = 5) \\ = > {a}^{3} + \frac{1}{ {a}^{3} } + 15 = 125 \\ = > {a}^{3} + \frac{1}{ {a}^{3} } = 125 - 15 \\ = > {a}^{3} + \frac{1}{ {a}^{3} } = 110$

Hence Proved