Question

2b^2x^2+3a^2y^2=a^2b^2 for b^2

Answer 1

Answer:

${b}^{2} = \frac{3 {a}^{2} {y}^{2} }{ {a}^{2} - 2 {x}^{2} }$

Step-by-step explanation:

We want to solve for b² in

$2 {b}^{2} {x}^{2} + 3 {a}^{2} {y}^{2} = {a}^{2} {b}^{2}$

Combine terms containing b²

$3 {a}^{2} {y}^{2} = {a}^{2} {b}^{2} - 2 {b}^{2} {x}^{2}$

Factor b² to get:

$3 {a}^{2} {y}^{2} = ({a}^{2} - 2 {x}^{2}) {b}^{2}$

Divide by a² -2b²

${b}^{2} = \frac{3 {a}^{2} {y}^{2} }{ {a}^{2} - 2 {x}^{2} }$