Answers

2015-10-30T14:08:17+05:30
Let 3^a = 5^b = 15^c = k

3^a = k  then 3 =  k^{ \frac{1}{a} }
5^b = k     then 5 =  k^{ \frac{1}{b} }
15^c = k  then 15 =  k^{ \frac{1}{c} }

15 = k^{ \frac{1}{c} }
5*3 = k^{ \frac{1}{c} }
k^{ \frac{1}{b} * k^{ \frac{1}{a} = k^{ \frac{1}{c} }
k^{ \frac{1}{b} + { \frac{1}{a} = k^{ \frac{1}{c} }

{ \frac{1}{b}+{ \frac{1}{a} = { \frac{1}{c} }

Squaring on both sides

 ({ \frac{1}{b}+{ \frac{1}{a})^{2}   = ({ \frac{1}{c} })^2

 \frac{1}{a^2} +  \frac{1}{b^2} + 2.  \frac{1}{a}. \frac{1}{a} =  \frac{1}{c^2}

 \frac{2}{ab} =  \frac{1}{c^2} - ( \frac{1}{a^2} +  \frac{1}{b^2} )


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