Solve l^612-1 - ScanMath

Question

Simplify the expression

12 l^{6} - 1

Evaluate

l^{6} \times 12 - 1

Solution

12 l^{6} - 1

Show Solution

l_{1} = - \frac{6 1 2 ^{5}}{12}, l_{2} = \frac{6 1 2 ^{5}}{12}

Alternative Form

l_{1} \approx - 0.660901, l_{2} \approx 0.660901

Evaluate

l^{6} \times 12 - 1

To find the roots of the expression,set the expression equal to 0

l^{6} \times 12 - 1 = 0

Use the commutative property to reorder the terms

12 l^{6} - 1 = 0

Move the constant to the right-hand side and change its sign

12 l^{6} = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

12 l^{6} = 1

Divide both sides

\frac{12 l ^{6}}{12} = \frac{1}{12}

Divide the numbers

l^{6} = \frac{1}{12}

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

l = \pm 6 \frac{1}{12}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{12}

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

\frac{6 1}{6 12}

Simplify the radical expression

\frac{1}{6 12}

Multiply by the Conjugate

\frac{6 1 2 ^{5}}{6 12 \times 6 1 2 ^{5}}

Multiply the numbers

More Steps

Evaluate

612 \times 6 1 2^{5}

The product of roots with the same index is equal to the root of the product

6 12 \times 1 2^{5}

Calculate the product

6 1 2^{6}

Reduce the index of the radical and exponent with 6

12

\frac{6 1 2 ^{5}}{12}

l = \pm \frac{6 1 2 ^{5}}{12}

Separate the equation into 2 possible cases

l = \frac{6 1 2 ^{5}}{12} l = - \frac{6 1 2 ^{5}}{12}

Solution

l_{1} = - \frac{6 1 2 ^{5}}{12}, l_{2} = \frac{6 1 2 ^{5}}{12}

Alternative Form

l_{1} \approx - 0.660901, l_{2} \approx 0.660901

Show Solution