Solve a^2≤3 - ScanMath

Evaluate

a^{2} \leq 3

Move the expression to the left side

a^{2} - 3 \leq 0

Rewrite the expression

a^{2} - 3 = 0

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

a^{2} = 0 + 3

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

a^{2} = 3

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

a = \pm 3

Separate the equation into 2 possible cases

a = 3 a = - 3

Determine the test intervals using the critical values

a < - 3 - 3 < a < 3 a > 3

Choose a value form each interval

a_{1} = - 3 a_{2} = 0 a_{3} = 3

To determine if a < - 3 is the solution to the inequality,test if the chosen value a = - 3 satisfies the initial inequality

More Steps

a < - 3 is not a solution a_{2} = 0 a_{3} = 3

To determine if - 3 < a < 3 is the solution to the inequality,test if the chosen value a = 0 satisfies the initial inequality

More Steps

a < - 3 is not a solution - 3 < a < 3 is the solution a_{3} = 3

To determine if a > 3 is the solution to the inequality,test if the chosen value a = 3 satisfies the initial inequality

More Steps

a < - 3 is not a solution - 3 < a < 3 is the solution a > 3 is not a solution

The original inequality is a nonstrict inequality,so include the critical value in the solution

- 3 \leq a \leq 3 is the solution

Solution

- 3 \leq a \leq 3

Alternative Form

a \in [- 3, 3]

Solve the inequality