Solve 81x^4 - 1 - ScanMath

Question

Factor the expression

(3 x - 1) (3 x + 1) (9 x^{2} + 1)

Evaluate

81 x^{4} - 1

Rewrite the expression in exponential form

(9 x^{2})^{2} - 1^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(9 x^{2} - 1) (9 x^{2} + 1)

Solution

More Steps

Evaluate

9 x^{2} - 1

Rewrite the expression in exponential form

(3 x)^{2} - 1^{2}

Use a^{2} - b^{2} = (a - b) (a + b) to factor the expression

(3 x - 1) (3 x + 1)

(3 x - 1) (3 x + 1) (9 x^{2} + 1)

Show Solution

x_{1} = - \frac{1}{3}, x_{2} = \frac{1}{3}

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0. \dot{3}

Evaluate

81 x^{4} - 1

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

81 x^{4} - 1 = 0

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

81 x^{4} = 0 + 1

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

81 x^{4} = 1

Divide both sides

\frac{81 x ^{4}}{81} = \frac{1}{81}

Divide the numbers

x^{4} = \frac{1}{81}

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

x = \pm 4 \frac{1}{81}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{81}

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

\frac{4 1}{4 81}

Simplify the radical expression

\frac{1}{4 81}

Simplify the radical expression

More Steps

Evaluate

481

Write the number in exponential form with the base of 3

4 3^{4}

Reduce the index of the radical and exponent with 4

3

\frac{1}{3}

x = \pm \frac{1}{3}

Separate the equation into 2 possible cases

x = \frac{1}{3} x = - \frac{1}{3}

Solution

x_{1} = - \frac{1}{3}, x_{2} = \frac{1}{3}

Alternative Form

x_{1} = - 0. \dot{3}, x_{2} = 0. \dot{3}

Show Solution