Question

If a = 5 + 2 root 6, then find the value of a² +1/a²
full explanation pls
it's urgent ​

Answer 1

Explanation:

$a^2 = (5+2\sqrt{6})^2=25 + 2(5)(2\sqrt{6})+(4)(6) = 25 + 20\sqrt{6}+24$

$a^2 = 49+ 20\sqrt{6}$

$\frac{1}{a^2} = (\frac{1}{a})^2 = (\frac{1}{5+2\sqrt{6}})^2=(\frac{1(5-2\sqrt{6})}{25 - 24})^2$ [ a^2 - b^2 = (a+b)(a-b)]

$\frac{1}{a^2}=(5-2\sqrt{6})^2 = 25 - 20\sqrt{6}+ 24 = 49 - 20\sqrt{6}$ [(a-b)^2 = a^2 - 2ab + b^2]

Hence,

$a^2+\frac{1}{a^2}= 49 + 20\sqrt{6}+49 - 20\sqrt{6}= 98$

Answer: 98