Question

2a^2-5b^2:ab=1:3 find a:b​

Answer 1

Answer:

$\frac{ {2a}^{2} - {5b}^{2} }{ab} = \frac{1}{3} \\ \\3( {2a}^{2} - {5b}^{2} ) = ab \\ \\ 6 {a}^{2} - 15 {b}^{2} = ab \\ \\ 6 {a}^{2} - ab - 15 {b}^{2} = 0 \\ \\ now \: factorising \: this \\ \\ {6a}^{2} + 9ab - 10ab - 15 {b}^{2} \\ \\ 3a(2a + 3b) - 5b(2a + 3b) \\ \\ (3a - 5b)(2a + 3b) \\ \\ 3a - 5b = 0 \\ \\ 3a = 5b \\ \\ a = \frac{5b}{3} \\ \\ b = \frac{3a}{5}$