Find the no. of values of x belongs to R for which

64^(1/x) + 48^(1/x) = 80^(1/x)

plzz give the full soln...

Dear Akhil

64^1/x + 48^1/x = 80^1/x

(8*8)^1/x + (8*6)^1/x = (8*10)^1/x

8^1/x*8^1/x + 8^1/x*6^1/x - 8^1/x*10^1/x = 0

taking 8^1/x common

8^1/x(8^1/x + 6^1/x - 10^1/x)=0

8^1/x= 0 or 8^1/x + 6^1/x - 10^1/x=0

8^1/x ≠0 for real x

hence 8^1/x + 6^1/x - 10^1/x=0

8^1/x + 6^1/x = 10^1/x

by inspection

x=1/2

so that 8² + 6² = 100 =10²

hence x=1/2

All the best.

AKASH GOYAL

AskiitiansExpert-IITD

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