Finite Math Examples

x^{2} + {(y - \sqrt[3]{x^{2}})}^{2} = 1

$x^{2} + {(y - \sqrt[3]{x^{2}})}^{2} = 1$

Step 1

Solve the equation for

y

$y$ .

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Step 1.1

Subtract

x^{2}

$x^{2}$ from both sides of the equation.

{(y - \sqrt[3]{x^{2}})}^{2} = 1 - x^{2}

${(y - \sqrt[3]{x^{2}})}^{2} = 1 - x^{2}$

Step 1.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

y - \sqrt[3]{x^{2}} = \pm \sqrt{1 - x^{2}}

$y - \sqrt[3]{x^{2}} = \pm \sqrt{1 - x^{2}}$

Step 1.3

Simplify

\pm \sqrt{1 - x^{2}}

$\pm \sqrt{1 - x^{2}}$ .

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Step 1.3.1

Rewrite

1

$1$ as

1^{2}

$1^{2}$ .

y - \sqrt[3]{x^{2}} = \pm \sqrt{1^{2} - x^{2}}

$y - \sqrt[3]{x^{2}} = \pm \sqrt{1^{2} - x^{2}}$

Step 1.3.2

Since both terms are perfect squares, factor using the difference of squares formula,

a^{2} - b^{2} = (a + b) (a - b)

$a^{2} - b^{2} = (a + b) (a - b)$ where

a = 1

$a = 1$ and

b = x

$b = x$ .

y - \sqrt[3]{x^{2}} = \pm \sqrt{(1 + x) (1 - x)}

$y - \sqrt[3]{x^{2}} = \pm \sqrt{(1 + x) (1 - x)}$

y - \sqrt[3]{x^{2}} = \pm \sqrt{(1 + x) (1 - x)}

$y - \sqrt[3]{x^{2}} = \pm \sqrt{(1 + x) (1 - x)}$

Step 1.4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 1.4.1

First, use the positive value of the

\pm

$\pm$ to find the first solution.

y - \sqrt[3]{x^{2}} = \sqrt{(1 + x) (1 - x)}

$y - \sqrt[3]{x^{2}} = \sqrt{(1 + x) (1 - x)}$

Step 1.4.2

Add

\sqrt[3]{x^{2}}

$\sqrt[3]{x^{2}}$ to both sides of the equation.

y = \sqrt{(1 + x) (1 - x)} + \sqrt[3]{x^{2}}

$y = \sqrt{(1 + x) (1 - x)} + \sqrt[3]{x^{2}}$

Step 1.4.3

Next, use the negative value of the

\pm

$\pm$ to find the second solution.

y - \sqrt[3]{x^{2}} = - \sqrt{(1 + x) (1 - x)}

$y - \sqrt[3]{x^{2}} = - \sqrt{(1 + x) (1 - x)}$

Step 1.4.4

Add

\sqrt[3]{x^{2}}

$\sqrt[3]{x^{2}}$ to both sides of the equation.

y = - \sqrt{(1 + x) (1 - x)} + \sqrt[3]{x^{2}}

$y = - \sqrt{(1 + x) (1 - x)} + \sqrt[3]{x^{2}}$

Step 1.4.5

The complete solution is the result of both the positive and negative portions of the solution.

y = \sqrt{(1 + x) (1 - x)} + \sqrt[3]{x^{2}}

$y = \sqrt{(1 + x) (1 - x)} + \sqrt[3]{x^{2}}$

y = - \sqrt{(1 + x) (1 - x)} + \sqrt[3]{x^{2}}

$y = - \sqrt{(1 + x) (1 - x)} + \sqrt[3]{x^{2}}$

y = \sqrt{(1 + x) (1 - x)} + \sqrt[3]{x^{2}}

$y = \sqrt{(1 + x) (1 - x)} + \sqrt[3]{x^{2}}$

y = - \sqrt{(1 + x) (1 - x)} + \sqrt[3]{x^{2}}

$y = - \sqrt{(1 + x) (1 - x)} + \sqrt[3]{x^{2}}$

y = \sqrt{(1 + x) (1 - x)} + \sqrt[3]{x^{2}}

$y = \sqrt{(1 + x) (1 - x)} + \sqrt[3]{x^{2}}$

y = - \sqrt{(1 + x) (1 - x)} + \sqrt[3]{x^{2}}

$y = - \sqrt{(1 + x) (1 - x)} + \sqrt[3]{x^{2}}$

Step 2

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be

0

$0$ or

1

$1$ for each of its variables. In this case, the degree of the variable in the equation violates the linear equation definition, which means that the equation is not a linear equation.

Not Linear