Question

if a =3+root5 /2 then find the value of a^2 +1/a^2​

Answer 1

Step-by-step explanation:

$\huge\bf{\mid{\overline{\underline{ANSWER:-}\mid}}} \\ \\ \huge\bold{Given:-} \\ \\ a = \frac{3 \sqrt{5}}{2} \\ \\ \huge\bold{Find:-} \\ \\ {a}^{2} + \frac{1}{{a}^{2}} \\ \\ Now, \\ \\ {a+b}^{2} = {a}^{2} + {b}^{2} + 2ab \\ \\ \implies {a + \frac{1}{a}}^{2} = {a}^{2} + \frac{1}{{a}^{2}} + 2 \frac{\cancel{a}}{\cancel{a}}$

$\implies {(3 + \sqrt{5} )}^{2} + \frac{1}{ {(3 + \sqrt{5} )}^{2} } + 2 \\ \\ \implies 9 + 5 + 6 \sqrt{5} + \frac{1}{ 9 + 5 + 6 \sqrt{5} } + 2 \\ \\ \implies 14 + 6 \sqrt{5} + \frac{1 }{14 + 6 \sqrt{5} } + 2 \\ \\ \implies \boxed{ \frac{404 + 12 \sqrt{5} }{14 + 6 \sqrt{5} } }$