Question

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

Answer 1

`{b}^(2) = \frac{3 {a}^(2) {y}^(2) }{ {a}^(2) - 2 {x}^(2) }`

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) }`