Question
If a : b = c : d, show that (2a - 7b) (2c + 7d) = (2c - 7d) (2a + 7b).
✓
Answer
We have
a: b = c : d
$\frac{a}{b}=\frac{c}{d}$
$\Rightarrow \frac{2 a}{7 b}=\frac{2 c}{7 d} \quad \ldots\left[\right.$ Multiplying both side $\left.\frac{2}{7}\right]$
[Using componendo and dividendo]
$\frac{2 a+7 b}{2 a-7 b}=\frac{2 c+7 d}{2 c-7 d} \quad \ldots$ [By cross multiplication $]$ $\Rightarrow(2 a-7 b)(2 c+7 d)=(2 a+7 b)(2 c-7 d)$.
Hence proved.
a: b = c : d
$\frac{a}{b}=\frac{c}{d}$
$\Rightarrow \frac{2 a}{7 b}=\frac{2 c}{7 d} \quad \ldots\left[\right.$ Multiplying both side $\left.\frac{2}{7}\right]$
[Using componendo and dividendo]
$\frac{2 a+7 b}{2 a-7 b}=\frac{2 c+7 d}{2 c-7 d} \quad \ldots$ [By cross multiplication $]$ $\Rightarrow(2 a-7 b)(2 c+7 d)=(2 a+7 b)(2 c-7 d)$.
Hence proved.
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