Solve r^4461-1 - ScanMath

Question

Simplify the expression

461 r^{4} - 1

Evaluate

r^{4} \times 461 - 1

Solution

461 r^{4} - 1

Show Solution

r_{1} = - \frac{4 46 1 ^{3}}{461}, r_{2} = \frac{4 46 1 ^{3}}{461}

Alternative Form

r_{1} \approx - 0.215812, r_{2} \approx 0.215812

Evaluate

r^{4} \times 461 - 1

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

r^{4} \times 461 - 1 = 0

Use the commutative property to reorder the terms

461 r^{4} - 1 = 0

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

461 r^{4} = 0 + 1

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

461 r^{4} = 1

Divide both sides

\frac{461 r ^{4}}{461} = \frac{1}{461}

Divide the numbers

r^{4} = \frac{1}{461}

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

r = \pm 4 \frac{1}{461}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{461}

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

\frac{4 1}{4 461}

Simplify the radical expression

\frac{1}{4 461}

Multiply by the Conjugate

\frac{4 46 1 ^{3}}{4 461 \times 4 46 1 ^{3}}

Multiply the numbers

More Steps

Evaluate

4461 \times 4 46 1^{3}

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

4 461 \times 46 1^{3}

Calculate the product

4 46 1^{4}

Reduce the index of the radical and exponent with 4

461

\frac{4 46 1 ^{3}}{461}

r = \pm \frac{4 46 1 ^{3}}{461}

Separate the equation into 2 possible cases

r = \frac{4 46 1 ^{3}}{461} r = - \frac{4 46 1 ^{3}}{461}

Solution

r_{1} = - \frac{4 46 1 ^{3}}{461}, r_{2} = \frac{4 46 1 ^{3}}{461}

Alternative Form

r_{1} \approx - 0.215812, r_{2} \approx 0.215812

Show Solution