If x = sqrt y/1+2y which of the following is equal to y? Answers A=1-x^2/x^2 , B= x^2/1-2x^2 , C=x^2/1+x^2, D= x^2/1+x^2, E=x^2/3

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Answer 1 · 2017-12-16T02:02:48

$y = \frac{x^{2}}{1 - 2 x^{2}}$ $y = x^2 /(1-2x^2)$

$x = {(\frac{y}{1 - 2 y^{2}})}^{\frac{1}{2}}$ $x = (y /(1-2y^2))^(1/2)$

Making ^2 both sides of eq:

$x^{2} = \frac{y}{1 - 2 y^{2}}$ $x^2 = y /(1-2y^2)$

Making inverse both sides of eq:

$\frac{1}{x^{2}} = \frac{1 + 2 y}{y}$ $1/x^2 = (1+2y) /y$

$\frac{1}{x^{2}} = \frac{1}{y} + 2$ $1/x^2 = 1/y+2$

Re-arranging for y:

$\frac{1}{y} = \frac{1}{x^{2}} - 2$ $1/y = 1/x^2-2$

$\frac{1}{y} = \frac{1 - 2 x^{2}}{x^{2}}$ $1/y = (1-2x^2)/x^2$

Making inverse both sides of eq:

$y = \frac{x^{2}}{1 - 2 x^{2}}$ $y = x^2 /(1-2x^2)$