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Question

Given the system of equations
(b+c)(y+z)ax=bc
(c+a)(z+x)by=ca
(a+b)(x+y)cz=ab
(where a+b+c0); then x:y:z is given by

A
cb:ac:ba
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B
b+c:c+a:a+b
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C
a:b:c
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D
ab:bc:ca
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Solution

The correct option is A cb:ac:ba
(b+c)(y+z)ax=bc ..............(1)

(c+a)(z+x)by=ca ..............(2)

(a+b)(x+y)cz=ab .............(3)

Adding all three equation
(x+y+z)(a+b+c)=0

x+y+z=0

y+z=x
Substituting this in the first (1) equation
(b+c)(x)ax=bc

x=cba+b+c
Similarly, we get
y=aca+b+c,z=baa+b+c
Hence x:y:z=(cb):(ac):(ba)

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