Question
If a : b : : c : d, prove that (2a + 3b)(2c – 3d) = (2a – 3b)(2c + 3d)
✓
Answer
$
\begin{aligned}
& \because a : b :: c : d \\
& \therefore \frac{a}{b}=\frac{c}{d} \\
& \Rightarrow \frac{2 a}{3 b}=\frac{2 c}{3 d} \ldots\left(\text { Multiply by } \frac{2}{3}\right)
\end{aligned}$
Applying componendo and dividendo,
$
\frac{2 a+3 b}{2 a-3 b}=\frac{2 c+3 d}{2 c-3 d}
$
$
\Rightarrow(2 a +3 b )(2 c -3 d )
$
$=(2 a-3 b)(2 c+3 d) \ldots($ By corss multiplication $)$.
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