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Question
If `(x + y)/(ax + by) = (y + z)/(ay + bz) = (z + x)/(az + bx)`, prove that each of these ratio is equal to `(2)/(a + b)` unless x + y + z = 0
Solution
`(x + y)/(ax + by) = (y + z)/(ay + bz) = (z + x)/(az + bx)`
= `(x+ y + y + z + z + x)/(ax + by + ay + bx + az + bx)`
= `(2(x y + z))/(x(a + b) + y(a + b) + z(a + b)`
= `(2(x + y + z))/((a + b)(x + y + z)`
= `(2)/(a + b)`
if x + y + z ≠ 0.
Hence proved.
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