Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Discover detailed solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
Sagot :
Let's consider the given equation:
[tex]\[ x^3 - 3x^2 - 4 = \frac{1}{x-1} + 5 \][/tex]
To solve for [tex]\( x \)[/tex], we simplify and solve the equation step-by-step.
1. First, move all terms to one side of the equation to set it equal to zero:
[tex]\[ x^3 - 3x^2 - 4 - \left( \frac{1}{x-1} + 5 \right) = 0 \][/tex]
2. Combine and simplify the terms on the left side:
[tex]\[ x^3 - 3x^2 - 4 - \frac{1}{x-1} - 5 = 0 \][/tex]
[tex]\[ x^3 - 3x^2 - 9 - \frac{1}{x-1} = 0 \][/tex]
3. Solve for [tex]\( x \)[/tex] to find the roots of the equation.
After solving, we obtain the following approximate solutions for [tex]\( x \)[/tex]:
[tex]\[ x \approx 3.68876, \quad x \approx -0.297742 \pm 1.51763i, \quad \text{and} \quad x \approx 0.906725 \][/tex]
Thus, the real solutions to the equation are approximately:
[tex]\[ x \approx 3.68876 \quad \text{and} \quad x \approx 0.906725 \][/tex]
Therefore, in the given drop-down menus, you should select:
- One drop-down to [tex]\( x \approx 3.68876 \)[/tex]
- The other drop-down to [tex]\( x \approx 0.906725 \)[/tex]
[tex]\[ x^3 - 3x^2 - 4 = \frac{1}{x-1} + 5 \][/tex]
To solve for [tex]\( x \)[/tex], we simplify and solve the equation step-by-step.
1. First, move all terms to one side of the equation to set it equal to zero:
[tex]\[ x^3 - 3x^2 - 4 - \left( \frac{1}{x-1} + 5 \right) = 0 \][/tex]
2. Combine and simplify the terms on the left side:
[tex]\[ x^3 - 3x^2 - 4 - \frac{1}{x-1} - 5 = 0 \][/tex]
[tex]\[ x^3 - 3x^2 - 9 - \frac{1}{x-1} = 0 \][/tex]
3. Solve for [tex]\( x \)[/tex] to find the roots of the equation.
After solving, we obtain the following approximate solutions for [tex]\( x \)[/tex]:
[tex]\[ x \approx 3.68876, \quad x \approx -0.297742 \pm 1.51763i, \quad \text{and} \quad x \approx 0.906725 \][/tex]
Thus, the real solutions to the equation are approximately:
[tex]\[ x \approx 3.68876 \quad \text{and} \quad x \approx 0.906725 \][/tex]
Therefore, in the given drop-down menus, you should select:
- One drop-down to [tex]\( x \approx 3.68876 \)[/tex]
- The other drop-down to [tex]\( x \approx 0.906725 \)[/tex]
Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.