Solve (y-2)(y^2)>y^2-5

Question

Solve the inequality

y > - 1.103803

Alternative Form

y \in (- 1.103803, + \infty)

Evaluate

(y - 2) y^{2} > y^{2} - 5

Multiply the terms

y^{2} (y - 2) > y^{2} - 5

Move the expression to the left side

y^{2} (y - 2) - (y^{2} - 5) > 0

Subtract the terms

More Steps

y^{3} - 3 y^{2} + 5 > 0

Rewrite the expression

y^{3} - 3 y^{2} + 5 = 0

Find the critical values by solving the corresponding equation

y \approx - 1.103803

Determine the test intervals using the critical values

y < - 1.103803 y > - 1.103803

Choose a value form each interval

y_{1} = - 2 y_{2} = 0

To determine if y < - 1.103803 is the solution to the inequality,test if the chosen value y = - 2 satisfies the initial inequality

More Steps

y < - 1.103803 is not a solution y_{2} = 0

To determine if y > - 1.103803 is the solution to the inequality,test if the chosen value y = 0 satisfies the initial inequality

More Steps

y < - 1.103803 is not a solution y > - 1.103803 is the solution

Solution

y > - 1.103803

Alternative Form

y \in (- 1.103803, + \infty)

Show Solution