Question

if a-1/a=√5 then find the values of a + 1/ a and a³ + 1/a³

Answer 1

Step-by-step explanation:

$a - \frac{1}{a} = \sqrt{5} \\ = > on \: squaring \: both \: sides \\ = > {(a - \frac{1}{a}) }^{2} = 5 \\ \\ = > {(a + \frac{1}{a} )}^{2} - 4 \times \frac{1}{a} \times a = 5 \\ \\ = > {(a + \frac{1}{a})}^{2} = 5 + 4 \\ \\ = > {(a + \frac{1}{a})}^{2} = 9 \\ \\ = > a + \frac{1}{a} = \binom{ + }{ - } 3$

Now,

$a + \frac{1}{a} = \binom{ + }{ - } 3 \\ \\ = > {(a + \frac{1}{a} )}^{3} = \binom{ + }{ - } 27 \\ \\ = > {a}^{3} + \frac{1}{ {a}^{3} } + 3a \times \frac{1}{a} (a + \frac{1}{a} ) = \binom{ + }{ - } 27 \\ \\ = > {a}^{3} + \frac{1}{ {a}^{3} } + 3 \times 3 = \binom{ + }{ - } 27 \\ \\ = > {a}^{3} + \frac{1}{ {a}^{3} } = \binom{ + }{ - } 27 - 9 \\ \\ = > {a}^{3} + \frac{1}{ {a}^{3} } = \binom{ +18 }{ -35 }$

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Answer 2

Answer:

this is the answer of the question