Solve 3y - 82y^5 - Socratic AI (ScanMath)

Question

Factor the expression

y (3 - 82 y^{4})

Evaluate

3 y - 82 y^{5}

Rewrite the expression

y \times 3 - y \times 82 y^{4}

Solution

y (3 - 82 y^{4})

Show Solution

y_{1} = - \frac{4 3 \times 8 2 ^{3}}{82}, y_{2} = 0, y_{3} = \frac{4 3 \times 8 2 ^{3}}{82}

Alternative Form

y_{1} \approx - 0.437348, y_{2} = 0, y_{3} \approx 0.437348

Evaluate

3 y - 82 y^{5}

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

3 y - 82 y^{5} = 0

Factor the expression

y (3 - 82 y^{4}) = 0

Separate the equation into 2 possible cases

y = 0 3 - 82 y^{4} = 0

Solve the equation

More Steps

Evaluate

3 - 82 y^{4} = 0

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

- 82 y^{4} = 0 - 3

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

- 82 y^{4} = - 3

Change the signs on both sides of the equation

82 y^{4} = 3

Divide both sides

\frac{82 y ^{4}}{82} = \frac{3}{82}

Divide the numbers

y^{4} = \frac{3}{82}

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

y = \pm 4 \frac{3}{82}

Simplify the expression

More Steps

Evaluate

4 \frac{3}{82}

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

\frac{4 3}{4 82}

Multiply by the Conjugate

\frac{4 3 \times 4 8 2 ^{3}}{4 82 \times 4 8 2 ^{3}}

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

\frac{4 3 \times 8 2 ^{3}}{4 82 \times 4 8 2 ^{3}}

Multiply the numbers

\frac{4 3 \times 8 2 ^{3}}{82}

y = \pm \frac{4 3 \times 8 2 ^{3}}{82}

Separate the equation into 2 possible cases

y = \frac{4 3 \times 8 2 ^{3}}{82} y = - \frac{4 3 \times 8 2 ^{3}}{82}

y = 0 y = \frac{4 3 \times 8 2 ^{3}}{82} y = - \frac{4 3 \times 8 2 ^{3}}{82}

Solution

y_{1} = - \frac{4 3 \times 8 2 ^{3}}{82}, y_{2} = 0, y_{3} = \frac{4 3 \times 8 2 ^{3}}{82}

Alternative Form

y_{1} \approx - 0.437348, y_{2} = 0, y_{3} \approx 0.437348

Show Solution