Answer:
[tex]{b}^{2} = \frac{3 {a}^{2} {y}^{2} }{ {a}^{2} - 2 {x}^{2} } [/tex]
Step-by-step explanation:
We want to solve for b² in
[tex]2 {b}^{2} {x}^{2} + 3 {a}^{2} {y}^{2} = {a}^{2} {b}^{2} [/tex]
Combine terms containing b²
[tex]3 {a}^{2} {y}^{2} = {a}^{2} {b}^{2} - 2 {b}^{2} {x}^{2}[/tex]
Factor b² to get:
[tex]3 {a}^{2} {y}^{2} = ({a}^{2} - 2 {x}^{2}) {b}^{2} [/tex]
Divide by a² -2b²
[tex] {b}^{2} = \frac{3 {a}^{2} {y}^{2} }{ {a}^{2} - 2 {x}^{2} } [/tex]
