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a^x=b^y=c^z and abc =1 prove that 1/x + 1/y + 1/z =1

a^x=b^y=c^z and abc =1 prove that 1/x + 1/y + 1/z =1

Grade:9

1 Answers

Soumya Ranjan Mohanty
117 Points
3 years ago
see question is wrong as 1/x + 1/y + 1/z = 0 , proving below:
 
let a^x=b^y=c^z=k => a=k^ (1/x) and b=k^ (1/y) and c=k^ (1/z)
as abc = 1 , k^(1/x)*k^(1/y)*k^(1/z)=1 => k^(1/x +1/y +1/z)=k^0
=> 1/x +1/y +1/z = 0 (proved) question given wrong, instead of 1, it should be 0.

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