Question

If $a/b=c/d$, prove $(a+b)/(c+d)$ = $\sqrt{ab/cd}$

Answer 1

Step-by-step explanation:

=>

$\frac{a}{b} = \frac{c}{d} \\ \frac{b}{d} = \frac{a}{c} \\ we \: have \: \frac{a}{b} = \frac{c}{d} \\ add \: 1 \: both \: side \\ \frac{a}{b} + 1 = \frac{c}{d} + 1 \\ \frac{a + b}{b} = \frac{c + d}{d} \\ \frac{a + b}{c + d} = \frac{b}{d} \\ \frac{a + b}{c + d} = \sqrt{ { \frac{b}{d} }^{2} } \\ \frac{a + b}{c + d} = \sqrt{ \frac{b}{d} \times \frac{b}{d} } \\ from \: above \: \frac{b}{d} = \frac{a}{c} \\ \frac{a + b}{c + d} = \sqrt{ \frac{a}{c} \times \frac{b}{d} }$