Answer to Question #294004 in Analytic Geometry for ubong

Question

x=5^1/4 5^-1/4 y=5^1/4 - 5^-1/4 prove that 5(x² y²)²=144?

Answer 1

$x=5^{\frac14} +5^{-\frac14}, y=5^{\frac14} -5^{-\frac14}$

$x^2=5^{\frac12} +5^{-\frac12}+2\\ y^2=5^{\frac12} +5^{-\frac12}-2\\ x^2-y^2=4\\ (x^2-y^2)^2=16\\ 5(x^2-y^2)^2=80$