Solve x^2 2x 1 > 0

Evaluate

x^{2} \times 2 x \times 1 > 0

Multiply the terms

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2 x^{3} > 0

Rewrite the expression

2 x^{3} = 0

Rewrite the expression

x^{2} \times 2 x \times 1 = 0

Multiply both sides

x^{2} \times 2 x \times 1 \times \frac{1}{2} = 0 \times \frac{1}{2}

Calculate

x^{2} \times x = 0

Separate the equation into 2 possible cases

x^{2} = 0 x = 0

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

x = 0 x = 0

Find the union

x = 0

Determine the test intervals using the critical values

x < 0 x > 0

Choose a value form each interval

x_{1} = - 1 x_{2} = 1

To determine if x < 0 is the solution to the inequality,test if the chosen value x = - 1 satisfies the initial inequality

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x < 0 is not a solution x_{2} = 1

To determine if x > 0 is the solution to the inequality,test if the chosen value x = 1 satisfies the initial inequality

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x < 0 is not a solution x > 0 is the solution

Solution

x > 0

Alternative Form

x \in (0, + \infty)

Solve the inequality