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Question
If 2x = 3y = 12z, show that `1/z=1/y+2/x`
Solution
Let 2x = 3y = 12z = k
`rArr2=k^(1/x),` `3=k^(1/y),` `12=k^(1/z)`
Now,
`12=k^(1/z)`
`rArr2^2xx3=k^(1/z)`
`rArr(k^(1/x))^2xxk^(1/y)=k^(1/z)`
`rArrk^(2/x+1/y)=k^(1/z)`
`rArr2/x+1/y=1/z`
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