Solve 2a(a^3)-1 - ScanMath

Question

Simplify the expression

2 a^{4} - 1

Evaluate

2 a \times a^{3} - 1

Solution

More Steps

Evaluate

2 a \times a^{3}

Multiply the terms with the same base by adding their exponents

2 a^{1 + 3}

Add the numbers

2 a^{4}

2 a^{4} - 1

Show Solution

a_{1} = - \frac{4 8}{2}, a_{2} = \frac{4 8}{2}

Alternative Form

a_{1} \approx - 0.840896, a_{2} \approx 0.840896

Evaluate

2 a (a^{3}) - 1

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

2 a (a^{3}) - 1 = 0

Calculate

2 a \times a^{3} - 1 = 0

Multiply

More Steps

Multiply the terms

2 a \times a^{3}

Multiply the terms with the same base by adding their exponents

2 a^{1 + 3}

Add the numbers

2 a^{4}

2 a^{4} - 1 = 0

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

2 a^{4} = 0 + 1

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

2 a^{4} = 1

Divide both sides

\frac{2 a ^{4}}{2} = \frac{1}{2}

Divide the numbers

a^{4} = \frac{1}{2}

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

a = \pm 4 \frac{1}{2}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{2}

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

\frac{4 1}{4 2}

Simplify the radical expression

\frac{1}{4 2}

Multiply by the Conjugate

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

Simplify

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

Multiply the numbers

More Steps

Evaluate

42 \times 4 2^{3}

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

4 2 \times 2^{3}

Calculate the product

4 2^{4}

Reduce the index of the radical and exponent with 4

2

\frac{4 8}{2}

a = \pm \frac{4 8}{2}

Separate the equation into 2 possible cases

a = \frac{4 8}{2} a = - \frac{4 8}{2}

Solution

a_{1} = - \frac{4 8}{2}, a_{2} = \frac{4 8}{2}

Alternative Form

a_{1} \approx - 0.840896, a_{2} \approx 0.840896

Show Solution