Solve 81x^4-16 - ScanMath

Question

Factor the expression

(3 x - 2) (3 x + 2) (9 x^{2} + 4)

Evaluate

81 x^{4} - 16

Rewrite the expression in exponential form

(9 x^{2})^{2} - (1 6^{\frac{1}{2}})^{2}

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

(9 x^{2} - 1 6^{\frac{1}{2}}) (9 x^{2} + 1 6^{\frac{1}{2}})

Evaluate

More Steps

Evaluate

9 x^{2} - 1 6^{\frac{1}{2}}

Calculate

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Evaluate

- 1 6^{\frac{1}{2}}

Rewrite in exponential form

- (2^{4})^{\frac{1}{2}}

Multiply the exponents

- 2^{4 \times \frac{1}{2}}

Multiply the exponents

- 2^{2}

Evaluate the power

- 4

9 x^{2} - 4

(9 x^{2} - 4) (9 x^{2} + 1 6^{\frac{1}{2}})

Evaluate

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Evaluate

9 x^{2} + 1 6^{\frac{1}{2}}

Calculate

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Evaluate

1 6^{\frac{1}{2}}

Rewrite in exponential form

(2^{4})^{\frac{1}{2}}

Multiply the exponents

2^{4 \times \frac{1}{2}}

Multiply the exponents

2^{2}

Evaluate the power

4

9 x^{2} + 4

(9 x^{2} - 4) (9 x^{2} + 4)

Solution

More Steps

Evaluate

9 x^{2} - 4

Rewrite the expression in exponential form

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

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

(3 x - 2) (3 x + 2)

(3 x - 2) (3 x + 2) (9 x^{2} + 4)

Show Solution

Find the roots

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

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 0. \dot{6}

Evaluate

81 x^{4} - 16

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

81 x^{4} - 16 = 0

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

81 x^{4} = 0 + 16

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

81 x^{4} = 16

Divide both sides

\frac{81 x ^{4}}{81} = \frac{16}{81}

Divide the numbers

x^{4} = \frac{16}{81}

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

x = \pm 4 \frac{16}{81}

Simplify the expression

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Evaluate

4 \frac{16}{81}

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

\frac{4 16}{4 81}

Simplify the radical expression

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Evaluate

416

Write the number in exponential form with the base of 2

4 2^{4}

Reduce the index of the radical and exponent with 4

2

\frac{2}{4 81}

Simplify the radical expression

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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{2}{3}

x = \pm \frac{2}{3}

Separate the equation into 2 possible cases

x = \frac{2}{3} x = - \frac{2}{3}

Solution

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

Alternative Form

x_{1} = - 0. \dot{6}, x_{2} = 0. \dot{6}

Show Solution