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if (x)/(a^(2)-b^(2))=(y)/(b^(2)-c^(2))=(...

if `(x)/(a^(2)-b^(2))=(y)/(b^(2)-c^(2))=(z)/(c^(2)-a^(2))`, then prove that x+y+z=0.

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let us assume that `(x)/(a^(2)-b^92))=(y)/(b^(2)-c^(2))=(z)/(c^(2)-a^(2))=k`
`impliesx=k(a^(2)-b^(2)),y=k(b^(2)-c^(2)) and z=k(c^(2)-a^(2))`
`impliesx+y+z=k(a^(2)-b^(2)+b^(2)-c^(2)+c^(2)-a^(2))`
`impliesx+y+z=k(0)`
`impliesx+y+z=0`
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