Solve (x^2 3)^2=4x^2 12

Question

Solve the equation

x_{1} = - \frac{4 3}{3}, x_{2} = 0, x_{3} = \frac{4 3}{3}

Alternative Form

x_{1} \approx - 2.309401, x_{2} = 0, x_{3} \approx 2.309401

Evaluate

(x^{2} \times 3)^{2} = 4 x^{2} \times 12

Simplify

More Steps

Evaluate

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

Use the commutative property to reorder the terms

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

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

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

Evaluate the power

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

Evaluate the power

More Steps

Evaluate

(x^{2})^{2}

Multiply the exponents

x^{2 \times 2}

Multiply the terms

x^{4}

9 x^{4}

9 x^{4} = 4 x^{2} \times 12

Multiply the terms

9 x^{4} = 48 x^{2}

Add or subtract both sides

9 x^{4} - 48 x^{2} = 0

Factor the expression

3 x^{2} (3 x^{2} - 16) = 0

Divide both sides

x^{2} (3 x^{2} - 16) = 0

Separate the equation into 2 possible cases

x^{2} = 0 3 x^{2} - 16 = 0

The only way a power can be 0 is when the base equals 0

x = 0 3 x^{2} - 16 = 0

Solve the equation

More Steps

Evaluate

3 x^{2} - 16 = 0

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

3 x^{2} = 0 + 16

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

3 x^{2} = 16

Divide both sides

\frac{3 x ^{2}}{3} = \frac{16}{3}

Divide the numbers

x^{2} = \frac{16}{3}

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

x = \pm \frac{16}{3}

Simplify the expression

More Steps

Evaluate

\frac{16}{3}

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

\frac{16}{3}

Simplify the radical expression

\frac{4}{3}

Multiply by the Conjugate

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

When a square root of an expression is multiplied by itself,the result is that expression

\frac{4 3}{3}

x = \pm \frac{4 3}{3}

Separate the equation into 2 possible cases

x = \frac{4 3}{3} x = - \frac{4 3}{3}

x = 0 x = \frac{4 3}{3} x = - \frac{4 3}{3}

Solution

x_{1} = - \frac{4 3}{3}, x_{2} = 0, x_{3} = \frac{4 3}{3}

Alternative Form

x_{1} \approx - 2.309401, x_{2} = 0, x_{3} \approx 2.309401

Show Solution