Solve (x^2 6)^2-3

Question

Simplify the expression

36 x^{4} - 3

Evaluate

(x^{2} \times 6)^{2} - 3

Use the commutative property to reorder the terms

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

Solution

36 x^{4} - 3

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Factor the expression

3 (12 x^{4} - 1)

Evaluate

(x^{2} \times 6)^{2} - 3

Use the commutative property to reorder the terms

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

Simplify

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Evaluate

(6 x^{2})^{2}

Rewrite the expression

6 x^{2} \times 6 x^{2}

Multiply the numbers

36 x^{2} \times x^{2}

Multiply the terms

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Evaluate

x^{2} \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{2 + 2}

Add the numbers

x^{4}

36 x^{4}

36 x^{4} - 3

Solution

3 (12 x^{4} - 1)

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Find the roots

x_{1} = - \frac{4 108}{6}, x_{2} = \frac{4 108}{6}

Alternative Form

x_{1} \approx - 0.537285, x_{2} \approx 0.537285

Evaluate

(x^{2} \times 6)^{2} - 3

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

(x^{2} \times 6)^{2} - 3 = 0

Use the commutative property to reorder the terms

(6 x^{2})^{2} - 3 = 0

Rewrite the expression

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Simplify

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

Rewrite the expression

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Evaluate

(6 x^{2})^{2}

To raise a product to a power,raise each factor to that power

6^{2} (x^{2})^{2}

Evaluate the power

36 (x^{2})^{2}

Evaluate the power

36 x^{4}

36 x^{4} - 3

36 x^{4} - 3 = 0

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

36 x^{4} = 0 + 3

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

36 x^{4} = 3

Divide both sides

\frac{36 x ^{4}}{36} = \frac{3}{36}

Divide the numbers

x^{4} = \frac{3}{36}

Cancel out the common factor 3

x^{4} = \frac{1}{12}

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

x = \pm 4 \frac{1}{12}

Simplify the expression

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Evaluate

4 \frac{1}{12}

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

\frac{4 1}{4 12}

Simplify the radical expression

\frac{1}{4 12}

Multiply by the Conjugate

\frac{4 1 2 ^{3}}{4 12 \times 4 1 2 ^{3}}

Simplify

\frac{2 4 108}{4 12 \times 4 1 2 ^{3}}

Multiply the numbers

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Evaluate

412 \times 4 1 2^{3}

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

4 12 \times 1 2^{3}

Calculate the product

4 1 2^{4}

Reduce the index of the radical and exponent with 4

12

\frac{2 4 108}{12}

Cancel out the common factor 2

\frac{4 108}{6}

x = \pm \frac{4 108}{6}

Separate the equation into 2 possible cases

x = \frac{4 108}{6} x = - \frac{4 108}{6}

Solution

x_{1} = - \frac{4 108}{6}, x_{2} = \frac{4 108}{6}

Alternative Form

x_{1} \approx - 0.537285, x_{2} \approx 0.537285

Show Solution