Solve x^2+( y_3\sqrt x^2)2=1

Question

Solve the equation

Solve for x

Solve for y_{3}

x = - y_{3} + y_{3}^{2} + 1 x = - y_{3} - y_{3}^{2} + 1

Evaluate

x^{2} + (y_{3} (x)^{2}) \times 2 = 1

Remove the parentheses

x^{2} + y_{3} (x)^{2} \times 2 = 1

Multiply the terms

More Steps

x^{2} + 2 y_{3} x = 1

Move the expression to the left side

x^{2} + 2 y_{3} x - 1 = 0

Substitute a= 1,b= 2 y_{3} and c= - 1 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 2 y _{3} \pm ( 2 y _{3} ) ^{2} - 4 ( - 1 )}{2}

Simplify the expression

More Steps

x = \frac{- 2 y _{3} \pm 4 y _{3}^{2} + 4}{2}

Simplify the radical expression

More Steps

x = \frac{- 2 y _{3} \pm 2 y _{3}^{2} + 1}{2}

Separate the equation into 2 possible cases

x = \frac{- 2 y _{3} + 2 y _{3}^{2} + 1}{2} x = \frac{- 2 y _{3} - 2 y _{3}^{2} + 1}{2}

Simplify the expression

More Steps

x = - y_{3} + y_{3}^{2} + 1 x = \frac{- 2 y _{3} - 2 y _{3}^{2} + 1}{2}

Solution

More Steps

x = - y_{3} + y_{3}^{2} + 1 x = - y_{3} - y_{3}^{2} + 1

Show Solution