If x : y = 10 : 3, find (3x² + 2y²) : (3x² − 2y²).

Given,

x : y = 10 : 3

Let x = 10a and y = 3a.

Substituting values in $\dfrac{3x^2 + 2y^2}{3x^2 − 2y^2}$ we get,

$\Rightarrow \dfrac{3(10a)^2 + 2(3a)^2}{3(10a)^2 - 2(3a)^2} \\[1em] \Rightarrow \dfrac{3(100a^2) + 2(9a^2)}{3(100a^2) - 2(9a^2)} \\[1em] \Rightarrow \dfrac{300a^2 + 18a^2}{300a^2 - 18a^2} \\[1em] \Rightarrow \dfrac{318a^2}{282a^2} \\[1em] \Rightarrow \dfrac{53}{47}.$

Hence, (3x² + 2y²) : (3x² − 2y²) = 53 : 47.