Question

if x= 7 + root 5 and y = 7 - root5​

Answer 1

$\huge {\mathcal{\purple{A}\green{N}\pink{S}\blue{W}\purple{E}\green{R}\pink{!}}}$

$here \: x = 7 + \sqrt{5} \: and \: y \: = 7 - \sqrt{5} \\ \\ then \\ \: {x}^{2} + {y}^{2} \\ \\ putting \: x = 7 + \sqrt{5} \: and \: y = 7 - \sqrt{5} \\ \\ = {(7 + \sqrt{5}) }^{2} + ({7 - \sqrt{5} )}^{2} \\ \\ we \: know \: that \\ \: {(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ \\ {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ \\ = {7}^{2} + { (\sqrt{5} )}^{2} + 2 \times 7 \times \sqrt{5} + {7}^{2} + { (\sqrt{5} )}^{2} - 2 \times 7 \times \sqrt{5} \\ \\ = 49 + 5 + 14 \sqrt{5} + 49 + 5 - 14 \sqrt{5} \\ \\ = 49 + 5 + 49 + 5 \\ \\ = 108$

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