Question

If a=5+2√6,then find the value of a²+1/a²

Answer 1

$a = 5 + 2 \sqrt{6} \\ {a}^{2} = 25 + 24 + 20 \sqrt{6} \\ = 49 + 20 \sqrt{6} \\ \\ {a}^{2} + \frac{1}{ {a}^{2} } =( 49 + 20 \sqrt{6} ) + \frac{1}{49 + 20 \sqrt{6} } \\ = (( {49 + 20 \sqrt{6} )}^{2} + 1) \div (49 + 20 \sqrt{6} ) \\ \frac{2401 + 2400 + 1960 \sqrt{6} + 1}{49 + 20 \sqrt{6} } \\ = \frac{4802 + 1960 \sqrt{6} }{49 + 20 \sqrt{6} }$
now do factorisation