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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
641/x + 481/x = 801/x
(8*8)1/x + (8*6)1/x = (8*10)1/x
81/x*81/x + 81/x*61/x - 81/x*101/x = 0
taking 81/x common
81/x(81/x + 61/x - 101/x)=0
81/x= 0 or 81/x + 61/x - 101/x=0
81/x ≠0 for real x
hence 81/x + 61/x - 101/x=0
81/x + 61/x = 101/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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