Question

if 2+√5/2-√5=x and 2-√5/2+√5=y then find x^2-y^2​

Answer 1

$\mathcal \red {{SOLUTION:-}}$

$\mathcal \orange{{ THE \: \: VALUE \: \: FOR \: \: X^2 \: \: AND \: \: Y^2 \: \: OBTAINED \: \: FROM \: \: ATTACHMENT}} \\ \mathcal \orange{{REFER \: \: ATTACHMENT \: \: FIRST}} \\ \\ \\ \tt \red { now, } \\ \\ \tt {x}^{2} = 161 + 72 \sqrt{5} \\ \tt {y}^{2} = 161 - 72 \sqrt{5} \\ \\ \tt {x} \: ^{2} - {y}^{2} \\ \\ \tt = 161 + 72 \sqrt{5} - (161 - 72 \sqrt{5} ) \\ \\ \tt = 161 + 72 \sqrt{5} - 161 + 72 \sqrt{5} \\ \\ \tt = 0 + 144 \sqrt{5} \\ \\ \tt {x}^{2} - {y}^{2} = 144 \sqrt{5} \: \: is \: answer.$