Solve (x^6)^2=x^2 x^2

Question

Solve the equation

x_{1} = - 1, x_{2} = 0, x_{3} = 1

Evaluate

(x^{6})^{2} = x^{2} \times x^{2}

Simplify

More Steps

Evaluate

(x^{6})^{2}

Multiply the exponents

x^{6 \times 2}

Multiply the numbers

x^{12}

x^{12} = 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}

x^{12} = x^{4}

Raise both sides of the equation to the reciprocal of the exponent

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

Evaluate the power

x^{3} = ∣ x ∣

Evaluate

x^{3} = x x^{3} = - x

Calculate

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Evaluate

x^{3} = x

Move the expression to the left side

x^{3} - x = 0

Factor the expression

x (x^{2} - 1) = 0

Separate the equation into 2 possible cases

x = 0 x^{2} - 1 = 0

Solve the equation

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Evaluate

x^{2} - 1 = 0

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

x^{2} = 0 + 1

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

x^{2} = 1

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

x = \pm 1

Simplify the expression

x = \pm 1

Separate the equation into 2 possible cases

x = 1 x = - 1

x = 0 x = 1 x = - 1

x = 0 x = 1 x = - 1 x^{3} = - x

Calculate

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Evaluate

x^{3} = - x

Move the expression to the left side

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

Add or subtract both sides

x^{3} + x = 0

Factor the expression

x (x^{2} + 1) = 0

Separate the equation into 2 possible cases

x = 0 x^{2} + 1 = 0

Solve the equation

More Steps

Evaluate

x^{2} + 1 = 0

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

x^{2} = 0 - 1

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

x^{2} = - 1

Since the left-hand side is always positive or 0,and the right-hand side is always negative,the statement is false for any value of x

x \in / R

x = 0 x \in / R

Find the union

x = 0

x = 0 x = 1 x = - 1 x = 0

Rearrange the terms

x = 0 x = 1 x = - 1

Solution

x_{1} = - 1, x_{2} = 0, x_{3} = 1

Show Solution