Question

If a=5+2 root 6 and b =1/A then what will be the value of a^2+b^2
and a^3+b^3

Answer 1

$a = 5 + 2 \sqrt{6} \\ b = \frac{1}{a} = \frac{1}{5 + 2 \sqrt{6} } \\ = > b = \frac{1}{5 + 2 \sqrt{6} } \times \frac{5 - 2 \ \sqrt{6} }{5 - 2 \sqrt{6} } \\ = > b = 5 - 2 \sqrt{6} \\ now \\ {a}^{2} + {b}^{2} = {(5 + 2 \sqrt{6}) }^{2} + {(5 - 2 \sqrt{6} )}^{2} \\ = > {a}^{2} + {b}^{2} = 98 \\ = > {a}^{3} + {b}^{3} = {(5 + 2 \sqrt{6} )}^{3} + {(5 - 2 \sqrt{6} )}^{3} \\ = > {a}^{3} + {b}^{3} = 1000 + 384 \sqrt{6}$
hope it helps