Solve a^48 - 3800/2017

Question

Simplify the expression

8 a^{4} - \frac{3800}{2017}

Evaluate

a^{4} \times 8 - \frac{3800}{2017}

Solution

8 a^{4} - \frac{3800}{2017}

Show Solution

\frac{8}{2017} (2017 a^{4} - 475)

Evaluate

a^{4} \times 8 - \frac{3800}{2017}

Use the commutative property to reorder the terms

8 a^{4} - \frac{3800}{2017}

Solution

\frac{8}{2017} (2017 a^{4} - 475)

Show Solution

a_{1} = - \frac{4 475 \times 201 7 ^{3}}{2017}, a_{2} = \frac{4 475 \times 201 7 ^{3}}{2017}

Alternative Form

a_{1} \approx - 0.696622, a_{2} \approx 0.696622

Evaluate

a^{4} \times 8 - \frac{3800}{2017}

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

a^{4} \times 8 - \frac{3800}{2017} = 0

Use the commutative property to reorder the terms

8 a^{4} - \frac{3800}{2017} = 0

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

8 a^{4} = 0 + \frac{3800}{2017}

Add the terms

8 a^{4} = \frac{3800}{2017}

Multiply by the reciprocal

8 a^{4} \times \frac{1}{8} = \frac{3800}{2017} \times \frac{1}{8}

Multiply

a^{4} = \frac{3800}{2017} \times \frac{1}{8}

Multiply

More Steps

Evaluate

\frac{3800}{2017} \times \frac{1}{8}

Reduce the numbers

\frac{475}{2017} \times 1

Multiply the numbers

\frac{475}{2017}

a^{4} = \frac{475}{2017}

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

a = \pm 4 \frac{475}{2017}

Simplify the expression

More Steps

Evaluate

4 \frac{475}{2017}

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

\frac{4 475}{4 2017}

Multiply by the Conjugate

\frac{4 475 \times 4 201 7 ^{3}}{4 2017 \times 4 201 7 ^{3}}

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

\frac{4 475 \times 201 7 ^{3}}{4 2017 \times 4 201 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

42017 \times 4 201 7^{3}

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

4 2017 \times 201 7^{3}

Calculate the product

4 201 7^{4}

Reduce the index of the radical and exponent with 4

2017

\frac{4 475 \times 201 7 ^{3}}{2017}

a = \pm \frac{4 475 \times 201 7 ^{3}}{2017}

Separate the equation into 2 possible cases

a = \frac{4 475 \times 201 7 ^{3}}{2017} a = - \frac{4 475 \times 201 7 ^{3}}{2017}

Solution

a_{1} = - \frac{4 475 \times 201 7 ^{3}}{2017}, a_{2} = \frac{4 475 \times 201 7 ^{3}}{2017}

Alternative Form

a_{1} \approx - 0.696622, a_{2} \approx 0.696622

Show Solution