Solve h*h^5-1<1 - ScanMath

Question

Solve the inequality

Solve the inequality by testing the values in the interval

Solve for h

- 62 < h < 62

Alternative Form

h \in (- 62, 62)

Evaluate

h \times h^{5} - 1 < 1

Multiply the terms

More Steps

h^{6} - 1 < 1

Move the expression to the left side

h^{6} - 1 - 1 < 0

Subtract the numbers

h^{6} - 2 < 0

Rewrite the expression

h^{6} - 2 = 0

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

h^{6} = 0 + 2

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

h^{6} = 2

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

h = \pm 62

Separate the equation into 2 possible cases

h = 62 h = - 62

Determine the test intervals using the critical values

h < - 62 - 62 < h < 62 h > 62

Choose a value form each interval

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

To determine if h < - 62 is the solution to the inequality,test if the chosen value h = - 2 satisfies the initial inequality

More Steps

h < - 62 is not a solution h_{2} = 0 h_{3} = 2

To determine if - 62 < h < 62 is the solution to the inequality,test if the chosen value h = 0 satisfies the initial inequality

More Steps

h < - 62 is not a solution - 62 < h < 62 is the solution h_{3} = 2

To determine if h > 62 is the solution to the inequality,test if the chosen value h = 2 satisfies the initial inequality

More Steps

h < - 62 is not a solution - 62 < h < 62 is the solution h > 62 is not a solution

Solution

- 62 < h < 62

Alternative Form

h \in (- 62, 62)

Show Solution