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Question

If (7a + 8b) (7c – 8d) = (7a – 8b) (7c + 8d);
Prove that a: b = c: d

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Solution

The given can the rewritten as
7a+8b7a=7c+8d7c8d
Applying componendo and dividendo, we have
7a+8b+7a8b7a+8b7a+8b=7c+8d+7c8d7c+8d7c+8d
14a16b=14c16d
ab=cd

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