If a b-c d then prove that a b-a 2-c 2 b 2-d 2

Let: #160;ab=cd=kThus, #160;we #160;have:a=bk #160;and #160;c=dkNow,L.H.S.=ab=kR.H.S. #160;=a2+c2b2+d2=bk2+dk2b2+d2 #160; #160; #160; #160; ...

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If a b=c d th...

Question

If $\frac{a}{b} = \frac{c}{d}$ then prove that $\frac{a}{b}$ = $\frac{\sqrt{a^{2} + c^{2}}}{\sqrt{b^{2} + d^{2}}}$

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(a^{2} + a c + c^{2}) (b^{2} + b d + d^{2}) = {(a b + b c + c d)}^{2}

If a, b, c, d are in GP, prove that

$(a^{2} + b^{2} + c^{2}) (b^{2} + c^{2} + d^{2}) = (a b + b c + c d)^{2}$

a, b, c, d

(a^{2} + b^{2} + c^{2}) (b^{2} + c^{2} + d^{2}) = (a b + b c + c d)^{2}

(a^{2} + b^{2} + c^{2}) (b^{2} + c^{2} + d^{2}) = (a b + b c + c d + d a)^{2}

(a^{2} + b^{2} + c^{2}) (b^{2} + c^{2} + d^{2}) = (a b + b c + c d)^{2}

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