|

Mathematics

If a : b = c : d, prove that (3a + 2b) : (3a − 2b) = (3c + 2d) : (3c − 2d).

Ratio Proportion

3 Likes

Answer

Given,

$\dfrac{a}{b} = \dfrac{c}{d}$

Multiplying both sides by $\dfrac{3}{2}$ ,

$\dfrac{3a}{2b} = \dfrac{3c}{2d}$

Applying componendo and dividendo:

$\dfrac{3a + 2b}{3a - 2b} = \dfrac{3c + 2d}{3c - 2d}$

Hence, proved that (3a + 2b) : (3a − 2b) = (3c + 2d) : (3c − 2d).

Answered By

2 Likes

Related Questions

If b is the mean proportion between a and c, show that:
$\dfrac{a^{4} + a^{2}b^{2} + b^{4}}{b^{4} + b^{2}c^{2} + c^{4}} = \dfrac{a^{2}}{c^{2}}$
View Answer