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Question
If ax = by = cz; prove that `x^2/"yz" + y^2/"zx" + z^2/"xy" = "bc"/a^2 + "ca"/b^2 + "ab"/c^2`
Solution
Let ax = by = cz = k
∴ x = `k/a, y = k/b, z = k/c`
L.H.S. = `x^2/"yz" + y^2/"zx" + z^2/"xy"`
= `(k^2/a^2)/(k/b.k/c) + (k^2/b^2)/(k/c.k/a) + (k^2/c^2)/(k/a.k/b)`
= `(k^2/a^2)/(k^2/"bc") + (k^2/b^2)/(k^2/"ca") + (k^2/c^2)/(k^2/"ab")`
= `k^2/a^2 xx "bc"/k^2 + k^2/b^2 xx "ca"/k^2 + k^2/c^2 xx "ab"/k^2`
= `"bc"/a^2 + "ca"/b^2 + "ab"/c^2`
= R.H.S.
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