a^-1/a=7, find a^4+1/a^4

Philip P. answered • 11/23/18

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a^-1/a = a^-1·a^-1 = a^-2 = 1/a² = 7, so a² = 1/7 and a⁴ = (1/7)² = 1/49

(a⁴+1)/a⁴ = a⁴/a⁴ + 1/a⁴ = 1 + (1/(1/49)) = 1 + 49 = 50

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