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Question

If bcy+z=acz+x=abx+y. then show that a(bc)yz=b(ca)zx=c(ab)xy

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Solution

let bcy+z ----Eq1

acz+x ----Eq2

abx+y ----Eq3
now,
subtract Eq3 from Eq1
bcaby+zxy [as they are equal}

subtract Eq1 from Eq2
acbcz+xyz [as they are equal}

subtract Eq2 from Eq2
abacx+yzx [as they are equal}

We Get,
a(bc)y+z=b(ca)zx=c(ab)x+y.

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