Solve 9f^4-3 - ScanMath

Question

Factor the expression

3 (3 f^{4} - 1)

Evaluate

9 f^{4} - 3

Solution

3 (3 f^{4} - 1)

Show Solution

f_{1} = - \frac{4 27}{3}, f_{2} = \frac{4 27}{3}

Alternative Form

f_{1} \approx - 0.759836, f_{2} \approx 0.759836

Evaluate

9 f^{4} - 3

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

9 f^{4} - 3 = 0

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

9 f^{4} = 0 + 3

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

9 f^{4} = 3

Divide both sides

\frac{9 f ^{4}}{9} = \frac{3}{9}

Divide the numbers

f^{4} = \frac{3}{9}

Cancel out the common factor 3

f^{4} = \frac{1}{3}

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

f = \pm 4 \frac{1}{3}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{3}

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

\frac{4 1}{4 3}

Simplify the radical expression

\frac{1}{4 3}

Multiply by the Conjugate

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

Simplify

\frac{4 27}{4 3 \times 4 3 ^{3}}

Multiply the numbers

More Steps

Evaluate

43 \times 4 3^{3}

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

4 3 \times 3^{3}

Calculate the product

4 3^{4}

Reduce the index of the radical and exponent with 4

3

\frac{4 27}{3}

f = \pm \frac{4 27}{3}

Separate the equation into 2 possible cases

f = \frac{4 27}{3} f = - \frac{4 27}{3}

Solution

f_{1} = - \frac{4 27}{3}, f_{2} = \frac{4 27}{3}

Alternative Form

f_{1} \approx - 0.759836, f_{2} \approx 0.759836

Show Solution