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Question

If ax1=bc,by1=ac,cz1=ab, then prove thatxy+yz+zxxyz=0.

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Solution

We have,

ax1=bc

ax=abc

a=(abc)1/x


Similarly,

b=(abc)1/y

c=(abc)1/z


Therefore,

abc=(abc)1/x.(abc)1/y.(abc)1/z

abc=(abc)1/x+1/y+1/z


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

xy+yz+zxxyz=1

xy+yz+zx=xyz

xy+yz+zxxyz=0



Hence, this is the answer.


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