Solve r^412-6-2 - ScanMath

Question

Simplify the expression

12 r^{4} - 8

Evaluate

r^{4} \times 12 - 6 - 2

Use the commutative property to reorder the terms

12 r^{4} - 6 - 2

Solution

12 r^{4} - 8

Show Solution

4 (3 r^{4} - 2)

Evaluate

r^{4} \times 12 - 6 - 2

Use the commutative property to reorder the terms

12 r^{4} - 6 - 2

Subtract the numbers

12 r^{4} - 8

Solution

4 (3 r^{4} - 2)

Show Solution

r_{1} = - \frac{4 54}{3}, r_{2} = \frac{4 54}{3}

Alternative Form

r_{1} \approx - 0.903602, r_{2} \approx 0.903602

Evaluate

r^{4} \times 12 - 6 - 2

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

r^{4} \times 12 - 6 - 2 = 0

Use the commutative property to reorder the terms

12 r^{4} - 6 - 2 = 0

Subtract the numbers

12 r^{4} - 8 = 0

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

12 r^{4} = 0 + 8

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

12 r^{4} = 8

Divide both sides

\frac{12 r ^{4}}{12} = \frac{8}{12}

Divide the numbers

r^{4} = \frac{8}{12}

Cancel out the common factor 4

r^{4} = \frac{2}{3}

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

r = \pm 4 \frac{2}{3}

Simplify the expression

More Steps

Evaluate

4 \frac{2}{3}

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

\frac{4 2}{4 3}

Multiply by the Conjugate

\frac{4 2 \times 4 3 ^{3}}{4 3 \times 4 3 ^{3}}

Simplify

\frac{4 2 \times 4 27}{4 3 \times 4 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

42 \times 427

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

4 2 \times 27

Calculate the product

454

\frac{4 54}{4 3 \times 4 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

43 \times 4 3^{3}

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

4 3 \times 3^{3}

Calculate the product

4 3^{4}

Reduce the index of the radical and exponent with 4

3

\frac{4 54}{3}

r = \pm \frac{4 54}{3}

Separate the equation into 2 possible cases

r = \frac{4 54}{3} r = - \frac{4 54}{3}

Solution

r_{1} = - \frac{4 54}{3}, r_{2} = \frac{4 54}{3}

Alternative Form

r_{1} \approx - 0.903602, r_{2} \approx 0.903602

Show Solution