Solve v*v^3-2≤1

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for v

- 43 \leq v \leq 43

Alternative Form

v \in [- 43, 43]

Evaluate

v \times v^{3} - 2 \leq 1

Multiply the terms

More Steps

v^{4} - 2 \leq 1

Move the expression to the left side

v^{4} - 2 - 1 \leq 0

Subtract the numbers

v^{4} - 3 \leq 0

Rewrite the expression

v^{4} - 3 = 0

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

v^{4} = 0 + 3

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

v^{4} = 3

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

v = \pm 43

Separate the equation into 2 possible cases

v = 43 v = - 43

Determine the test intervals using the critical values

v < - 43 - 43 < v < 43 v > 43

Choose a value form each interval

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

To determine if v < - 43 is the solution to the inequality,test if the chosen value v = - 2 satisfies the initial inequality

More Steps

v < - 43 is not a solution v_{2} = 0 v_{3} = 2

To determine if - 43 < v < 43 is the solution to the inequality,test if the chosen value v = 0 satisfies the initial inequality

More Steps

v < - 43 is not a solution - 43 < v < 43 is the solution v_{3} = 2

To determine if v > 43 is the solution to the inequality,test if the chosen value v = 2 satisfies the initial inequality

More Steps

v < - 43 is not a solution - 43 < v < 43 is the solution v > 43 is not a solution

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

- 43 \leq v \leq 43 is the solution

Solution

- 43 \leq v \leq 43

Alternative Form

v \in [- 43, 43]

Show Solution