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Question

If ax1=bc, by1=ac, cz1=ab such that x,y,z are integers then value of xy+yz+zxxyz is

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Solution

ax1=bc

axa=bc

ax=abc

a=(abc)1x---------(1)

by1=ac

byb=ac

by=abc

b=(abc)1y-----(2)

cz1=ab

czc=ab

cy=abc

c=(abc)1z-------(3)

Now, from equations (1), (2) and (3),

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

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

1x+1y+1y=1

xy+yz+zxxyz=1

xy+yz+zx=xyz

xy+yz+zxxyz=0


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