Question
If (4a + 9b) (4c – 9d) = (4a – 9b) (4c + 9d), prove that: a: b = c: d.
✓
Answer
Given $\frac{4 a+9 b}{4 a-9 b}=\frac{4 c+9 d}{4 c-9 d}$
Applying componendo and dividendo
$\frac{4 a+9 b+4 a-9 b}{4 a+9 b-4 a+9 b}=\frac{4 c+9 d+4 c-9 d}{4 c+9 d-4 c+9 d}$
$\frac{8 a}{18 b}=\frac{8 c}{18 d}$
$\frac{a}{b}=\frac{c}{d}$
Applying componendo and dividendo
$\frac{4 a+9 b+4 a-9 b}{4 a+9 b-4 a+9 b}=\frac{4 c+9 d+4 c-9 d}{4 c+9 d-4 c+9 d}$
$\frac{8 a}{18 b}=\frac{8 c}{18 d}$
$\frac{a}{b}=\frac{c}{d}$
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