Question

If x:y = 2:5, then determine the following ratio : $x^2 + 2y^2 - xy:2x^2 + 3y^2 + 5xy$

Answer 1

Step-by-step explanation:

$\small{ = > \frac{{x}^{2} + 2{y}^{2} - xy }{ {2x}^{2} + 3 {y}^{2} + 5xy } } \\ \\ \small{ = > \frac{ \frac{ {x}^{2} + 2y {}^{2} - xy }{y {}^{2} } }{ \frac{{2x}^{2} + 3 {y}^{2} + 5xy }{ {y}^{2} }} } \\ \\ \small{ = > \frac{ \frac{x {}^{2} }{y {}^{2} } + \frac{2y {}^{2} }{ { {y}^{2} }^{} } - \frac{xy}{y {}^{2} } }{\frac{2x{}^{2} }{y {}^{2} } + \frac{3y {}^{2} }{ { {y}^{2} }^{} } + \frac{5xy}{y {}^{2} }} } \\ \\ \small{ = > \frac{ (\frac{x}{y} ) {}^{2} + 2 - \frac{x}{y} }{2( \frac{x }{y} ) {}^{2} + 3 + \frac{5x}{y} } } \\ \\ \small{ = > \frac{ \frac{2 {}^{2} }{5 {}^{2} } + 2 - \frac{2}{5} }{2( \frac{2 {}^{2} }{5 {}^{2}} ) {}^{} + 3 + 5( \frac{2}{5} ) } } \\ \\ \small{ = > \frac{ \frac{4 + 50 -10}{25} }{ \frac{8 + 75 + 50}{25} } } \\ \\ \small{ = > \frac{44}{133} }$