My Math Forum Ratio and Proportion I

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 March 18th, 2013, 06:50 AM #1 Senior Member   Joined: Feb 2013 Posts: 114 Thanks: 0 Ratio and Proportion I If a,b,c,d are in continued proportion, prove that : $(\frac{a-b}{c}+\frac{a-c}{b})^2-(\frac{d-b}{c}+\frac{d-c}{b})^2=(a-d)^2(\frac{1}{c^2}-\frac{1}{b^2})^2$ After solving L.H.S I got :$\frac{2(a-d)}{(bc)^2}$ But after solving R.H.S I am getting $\frac{(a-d)^2(b^2-c^2)}{(bc)^2}$... Please help.
 March 18th, 2013, 09:35 PM #2 Global Moderator   Joined: Dec 2006 Posts: 19,065 Thanks: 1621 As a/b = b/c and c/b = d/c, first square term of LHS = (a/c - b/c + a/b - c/b)² = (a/c - d/c)² = ((a - d)/c)². Similarly, the second square term of LHS = ((d - a)/b)². The rest is easy.

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