If a : b = c : d, prove that: (9a + 13b) (9c – 13d) = (9c + 13d) … - Vidyadip

Question

If a : b = c : d, prove that: (9a + 13b) (9c – 13d) = (9c + 13d) (9a – 13b).

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Answer

Given $\frac{a}{b}=\frac{c}{d}$
$\Rightarrow \frac{9 a}{13 b}=\frac{9 c}{13 d}$ (Multiplying each side by $9 / 13$ )
$\Rightarrow \frac{9 a+13 b}{13 a-13 b}=\frac{9 c+13 d}{9 c-13 d}$ (By componendo and divdendo)
$\Rightarrow(9 a+13 b)(9 c-13 d)=(9 c+13 d)(9 a-13 b)$

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