Question

जर ${\displaystyle \frac{a}{b}=\frac{b}{c}}$ आणि a, b, c > 0 तर सिद्ध करा की, ${\displaystyle \frac{a^2+b^2}{ab}=\frac{a+c}{b}}$

Answer 1

${\displaystyle \frac{a}{b}=\frac{b}{c}\Rightarrow b^2=ac}$    ...(1)

डावी बाजू = ${\displaystyle \frac{a^2+b^2}{ab}}$

= ${\displaystyle \frac{a^2+ac}{ab}}$   ...[1 वरून]

= ${\displaystyle \frac{a(a+c)}{ab}}$

= ${\displaystyle \frac{a+c}{b}}$

उजवी बाजू = ${\displaystyle \frac{a+c}{b}}$

∴ डावी बाजू = उजवी बाजू

∴ ${\displaystyle \frac{a^2+b^2}{ab}=\frac{a+c}{b}}$