Solve 65v^5-v - ScanMath

Question

Factor the expression

v (65 v^{4} - 1)

Evaluate

65 v^{5} - v

Rewrite the expression

v \times 65 v^{4} - v

Solution

v (65 v^{4} - 1)

Show Solution

v_{1} = - \frac{4 6 5 ^{3}}{65}, v_{2} = 0, v_{3} = \frac{4 6 5 ^{3}}{65}

Alternative Form

v_{1} \approx - 0.352186, v_{2} = 0, v_{3} \approx 0.352186

Evaluate

65 v^{5} - v

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

65 v^{5} - v = 0

Factor the expression

v (65 v^{4} - 1) = 0

Separate the equation into 2 possible cases

v = 0 65 v^{4} - 1 = 0

Solve the equation

More Steps

Evaluate

65 v^{4} - 1 = 0

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

65 v^{4} = 0 + 1

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

65 v^{4} = 1

Divide both sides

\frac{65 v ^{4}}{65} = \frac{1}{65}

Divide the numbers

v^{4} = \frac{1}{65}

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

v = \pm 4 \frac{1}{65}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{65}

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

\frac{4 1}{4 65}

Simplify the radical expression

\frac{1}{4 65}

Multiply by the Conjugate

\frac{4 6 5 ^{3}}{4 65 \times 4 6 5 ^{3}}

Multiply the numbers

\frac{4 6 5 ^{3}}{65}

v = \pm \frac{4 6 5 ^{3}}{65}

Separate the equation into 2 possible cases

v = \frac{4 6 5 ^{3}}{65} v = - \frac{4 6 5 ^{3}}{65}

v = 0 v = \frac{4 6 5 ^{3}}{65} v = - \frac{4 6 5 ^{3}}{65}

Solution

v_{1} = - \frac{4 6 5 ^{3}}{65}, v_{2} = 0, v_{3} = \frac{4 6 5 ^{3}}{65}

Alternative Form

v_{1} \approx - 0.352186, v_{2} = 0, v_{3} \approx 0.352186

Show Solution