Question

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

prove that

$bdf( \frac{a + b}{b} + \frac{c + d}{d} + \frac{e + f}{f} ) ^{3} = 27(a + b) \: (c + d) \: (e + f)$

Answer 1

$bdf( \frac{a + b}{b} + \frac{c + d}{d} + \frac{e + f}{f} ) ^{3} \\ = bdf( \frac{a }{b} + 1 + \frac{c}{d} + 1 + \frac{e}{f} + 1) ^{3} \\ = bdf( 3(\frac{a }{b})+ 3) ^{3} \\ = bdf \times 27( \frac{a }{b}+ 1) ^{3} \\ =27(b)( \frac{a }{b}+ 1) \times (d)( \frac{c }{d}+ 1) \times (f)( \frac{e }{f}+ 1) \\ = \boxed{ 27(a + b)(c + d)(e + f)}$
Hence Proved.

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Answer 2

Answer:

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Step-by-step explanation:

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