Solve r^4412-4 - ScanMath

Question

Simplify the expression

412 r^{4} - 4

Evaluate

r^{4} \times 412 - 4

Solution

412 r^{4} - 4

Show Solution

4 (103 r^{4} - 1)

Evaluate

r^{4} \times 412 - 4

Use the commutative property to reorder the terms

412 r^{4} - 4

Solution

4 (103 r^{4} - 1)

Show Solution

r_{1} = - \frac{4 10 3 ^{3}}{103}, r_{2} = \frac{4 10 3 ^{3}}{103}

Alternative Form

r_{1} \approx - 0.3139, r_{2} \approx 0.3139

Evaluate

r^{4} \times 412 - 4

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

r^{4} \times 412 - 4 = 0

Use the commutative property to reorder the terms

412 r^{4} - 4 = 0

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

412 r^{4} = 0 + 4

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

412 r^{4} = 4

Divide both sides

\frac{412 r ^{4}}{412} = \frac{4}{412}

Divide the numbers

r^{4} = \frac{4}{412}

Cancel out the common factor 4

r^{4} = \frac{1}{103}

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

r = \pm 4 \frac{1}{103}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{103}

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

\frac{4 1}{4 103}

Simplify the radical expression

\frac{1}{4 103}

Multiply by the Conjugate

\frac{4 10 3 ^{3}}{4 103 \times 4 10 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

4103 \times 4 10 3^{3}

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

4 103 \times 10 3^{3}

Calculate the product

4 10 3^{4}

Reduce the index of the radical and exponent with 4

103

\frac{4 10 3 ^{3}}{103}

r = \pm \frac{4 10 3 ^{3}}{103}

Separate the equation into 2 possible cases

r = \frac{4 10 3 ^{3}}{103} r = - \frac{4 10 3 ^{3}}{103}

Solution

r_{1} = - \frac{4 10 3 ^{3}}{103}, r_{2} = \frac{4 10 3 ^{3}}{103}

Alternative Form

r_{1} \approx - 0.3139, r_{2} \approx 0.3139

Show Solution