Question #294004

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

1
Expert's answer
2022-02-07T13:55:13-0500

x=514+514,y=514514x=5^{\frac14} +5^{-\frac14}, y=5^{\frac14} -5^{-\frac14}

x2=512+512+2y2=512+5122x2y2=4(x2y2)2=165(x2y2)2=80x^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


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