Question

a/b=c/d=e/f to solve bdf[a+b/b + c+d/d + e+f/f] ³

Answer 1

I hope you will be able to get the answer

Answer 2

∴ The value is $27bdf[\frac{a}{b} +1]^{3}$

Step-by-step explanation:

Given;

$\frac{a}{b}=\frac{c}{d}=\frac{e}{f}$ then $bdf[\frac{a+b}{b} +\frac{c+d}{d} + \frac{e+f}{f} ]^{3}=?$

Let,

$\frac{a}{b}=\frac{c}{d}=\frac{e}{f}=k$

Then, $a=bk$ , $c=dk$ and $e=fk$

∴ $bdf[\frac{a+b}{b} +\frac{c+d}{d} + \frac{e+f}{f} ]^{3}$

Plug all value in above equation;

$=bdf[\frac{bk+b}{b} +\frac{dk+d}{d} + \frac{fk+f}{f} ]^{3}$

$=bdf[\frac{b(k+1)}{b} +\frac{d(k+1)}{d} + \frac{f(k+1)}{f} ]^{3}$

$=bdf[(k+1)+(k+1)+(k+1)]^{3}$

$=bdf[3(k+1)]^{3}$

$=27bdf[k+1]^{3}$

$=27bdf[\frac{a}{b} +1]^{3}$  (∵$k=\frac{a}{b}$ )

∴ The value is $27bdf[\frac{a}{b} +1]^{3}$