Question

if ax = by = cz and abc 1 then prove that xy+ yz+ zx=0
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Answer 1

Hi Guys, I am new to Quora..I love the enviroment here …. This answer can be done by taking logs as well ..However guys I have done it in the most simple way possible ..Feel free to ask me anything if you don't understand .

Let a^x=b^y=c^z=k

Therefore,

a=k^(1/x)

b=k^(1/y)

c=k^(1/z)

As abc=1

k^(1/x).k^(1/y).k^(1/z)=1

k^(1/x+1/y+1/z)= 1 or k^0( as any number to the power 0 is 1)

Comparing the powers we get

1/x+1/y+1/z=0

Or

(yz+xz+xy)/xyz=0

Or xy+yz+zx=0 hence proved :)

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