Question

Despeja la variable "y" y "x" de la ecuación siguiente:
4x2-9y2=36​

Answer 1

Explicación paso a paso:

$4 {x}^{2} - 9 {y}^{2} = 36 \\ 4 {x}^{2} = 36 - 9 {y}^{2} \\ {x}^{2} = \frac{36 - 9 {y}^{2} }{4} \\ \sqrt{ {x}^{2} } = \sqrt{ \frac{36 - 9 {y}^{2} }{4} } \\ x = \sqrt{ \frac{36 - 9 {y}^{2} }{4} } \\ x = \frac{1}{2} \sqrt{ 36 - 9 {y}^{2} } \\ x = \frac{1}{2} \sqrt{9(4 - {y}^{2}) } \\ x = \frac{3}{2} \sqrt{4 - {y}^{2} }$

$4 {x}^{2} - 9 {y}^{2} = 36 \\ - 9 {y}^{2} = 36 - 4 {x}^{2} \\ 9 {y }^{2} = 4 {x }^{2} - 36 \\ {y}^{2} = \frac{4 {x}^{2} - 36}{9} \\ \sqrt{ {y}^{2} } = \sqrt{ \frac{4 {x}^{2} - 36}{9} } \\ y = \frac{1}{3} \sqrt{4 {x}^{2} - 36 } \\ y = \frac{1}{3} \sqrt{4( {x}^{2} - 9) } \\ y = \frac{2}{3} \sqrt{ {x}^{2} - 9}$