Question

24(3a^2-b^2)=37ab then a:b is?​

Answer 1

Given:

$24(3a^{2}-b^{2})=37ab$

To find: $a:b$

Step-by-step explanation:

Given, $24(3a^{2}-b^{2})=37ab$

$\Rightarrow 72a^{2}-24b^{2}=37ab$

• take all the terms in the left hand side

$\Rightarrow 72a^{2}-24b^{2}-37ab=0$

• rearrange the terms for a middle term factorization

$\Rightarrow 72a^{2}-37ab-24b^{2}=0$

$\Rightarrow 72a^{2}-(64-27)ab-24b^{2}=0$

$\Rightarrow 72a^{2}-64ab+27ab-24b^{2}=0$

$\Rightarrow 8a(9a-8b)+3b(9a-8b)=0$

$\Rightarrow (9a-8b)(8a+3b)=0$

$\therefore$ either $9a-8b=0$ or, $8a+3b=0$

$\Rightarrow 9a=8b$ or, $8a=-3b$

In order to find the ratio of $a$ and $b$, we take only the positive value.

i.e., $9a=8b$

$\Rightarrow \dfrac{a}{b}=\dfrac{8}{9}$

$\Rightarrow a:b=8:9$

Answer: $a:b=8:9$