Solve n12 = n1/n^2

Question

Solve the equation

n_{1} = - \frac{3}{6}, n_{2} = \frac{3}{6}

Alternative Form

n_{1} \approx - 0.288675, n_{2} \approx 0.288675

Evaluate

n \times 12 = n \times \frac{1}{n ^{2}}

Find the domain

More Steps

Evaluate

n^{2} \neq = 0

The only way a power can not be 0 is when the base not equals 0

n \neq = 0

n \times 12 = n \times \frac{1}{n ^{2}}, n \neq = 0

Use the commutative property to reorder the terms

12 n = n \times \frac{1}{n ^{2}}

Multiply the terms

More Steps

Multiply the terms

n \times \frac{1}{n ^{2}}

Cancel out the common factor n

1 \times \frac{1}{n}

Multiply the terms

\frac{1}{n}

12 n = \frac{1}{n}

Cross multiply

12 n \times n = 1

Simplify the equation

12 n^{2} = 1

Divide both sides

\frac{12 n ^{2}}{12} = \frac{1}{12}

Divide the numbers

n^{2} = \frac{1}{12}

Take the root of both sides of the equation and remember to use both positive and negative roots

n = \pm \frac{1}{12}

Simplify the expression

More Steps

Evaluate

\frac{1}{12}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{1}{12}

Simplify the radical expression

\frac{1}{12}

Simplify the radical expression

More Steps

Evaluate

12

Write the expression as a product where the root of one of the factors can be evaluated

4 \times 3

Write the number in exponential form with the base of 2

2^{2} \times 3

The root of a product is equal to the product of the roots of each factor

2^{2} \times 3

Reduce the index of the radical and exponent with 2

23

\frac{1}{2 3}

Multiply by the Conjugate

\frac{3}{2 3 \times 3}

Multiply the numbers

More Steps

Evaluate

23 \times 3

When a square root of an expression is multiplied by itself,the result is that expression

2 \times 3

Multiply the terms

6

\frac{3}{6}

n = \pm \frac{3}{6}

Separate the equation into 2 possible cases

n = \frac{3}{6} n = - \frac{3}{6}

Check if the solution is in the defined range

n = \frac{3}{6} n = - \frac{3}{6}, n \neq = 0

Find the intersection of the solution and the defined range

n = \frac{3}{6} n = - \frac{3}{6}

Solution

n_{1} = - \frac{3}{6}, n_{2} = \frac{3}{6}

Alternative Form

n_{1} \approx - 0.288675, n_{2} \approx 0.288675

Show Solution