Solve dd^3024-1 - ScanMath

Question

Simplify the expression

24 d^{4} - 1

Evaluate

d \times d^{3} \times 24 - 1

Solution

More Steps

Evaluate

d \times d^{3} \times 24

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 24

Add the numbers

d^{4} \times 24

Use the commutative property to reorder the terms

24 d^{4}

24 d^{4} - 1

Show Solution

d_{1} = - \frac{4 54}{6}, d_{2} = \frac{4 54}{6}

Alternative Form

d_{1} \approx - 0.451801, d_{2} \approx 0.451801

Evaluate

d \times d^{3} \times 24 - 1

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

d \times d^{3} \times 24 - 1 = 0

Multiply

More Steps

Multiply the terms

d \times d^{3} \times 24

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 24

Add the numbers

d^{4} \times 24

Use the commutative property to reorder the terms

24 d^{4}

24 d^{4} - 1 = 0

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

24 d^{4} = 0 + 1

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

24 d^{4} = 1

Divide both sides

\frac{24 d ^{4}}{24} = \frac{1}{24}

Divide the numbers

d^{4} = \frac{1}{24}

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

d = \pm 4 \frac{1}{24}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{24}

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

\frac{4 1}{4 24}

Simplify the radical expression

\frac{1}{4 24}

Multiply by the Conjugate

\frac{4 2 4 ^{3}}{4 24 \times 4 2 4 ^{3}}

Simplify

\frac{4 4 54}{4 24 \times 4 2 4 ^{3}}

Multiply the numbers

More Steps

Evaluate

424 \times 4 2 4^{3}

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

4 24 \times 2 4^{3}

Calculate the product

4 2 4^{4}

Reduce the index of the radical and exponent with 4

24

\frac{4 4 54}{24}

Cancel out the common factor 4

\frac{4 54}{6}

d = \pm \frac{4 54}{6}

Separate the equation into 2 possible cases

d = \frac{4 54}{6} d = - \frac{4 54}{6}

Solution

d_{1} = - \frac{4 54}{6}, d_{2} = \frac{4 54}{6}

Alternative Form

d_{1} \approx - 0.451801, d_{2} \approx 0.451801

Show Solution