Question

20 points, please help I really bloody need it

2. The equation x+2= v-----3x+10 is of the form x+a=v------bx+c ,where a, b, and c are all positive integers and b>1. Using this equation as a model, create your own equation that has extraneous solutions.
(a) Using trial and error with numbers for a, b, and c, create an equation of the form x+a=v-----bx+c, where a, b, and c are all positive integers and b>1 such that 7 is a solution. (Hint: Substitute 7 for x, and choose a value for a. Then square both sides so you can choose a, b, and c that will make the equation true.)
(b) Solve the equation you created in Part 2a.

(c) If your solution in Part 2b did not have an extraneous solution, revise your equation so that 7 is one solution and there is an extraneous solution. If your solution in Part 2b did have an extraneous solution, create another equation with different values of a, b, and c that also has 7 as one solution and an extraneous solution.

Answer 1

To create an equation with extraneous solutions of the form x+a=v-----bx+c, you can choose values for a, b, and c that make the equation true for a certain value of x and then square both sides of the equation to create extraneous solutions.

Step-by-step explanation:

To create an equation of the form x+a=v-----bx+c with extraneous solutions, we need to choose values for a, b, and c that will make the equation true for a particular value of x, but also yield extraneous solutions when solving the equation. To demonstrate this, let's choose a = 3, b = 13, and c = -10. Our equation becomes x + 3 = v ----- 13x - 10.

To solve this equation, we can substitute x = 7 and solve for v. When we do this, we get 7 + 3 = v. Therefore, v = 10. So one solution of the equation is x = 7 and v = 10.

Now, let's square both sides of the equation x + 3 = v ----- 13x - 10 to create an equation that will yield extraneous solutions. Squaring both sides gives us (x + 3)² = (v ----- 13x - 10)². When we expand this equation, we get x² + 6x + 9 = v² - 26vx + 169x² - 20v + 100. Simplifying further, we get x² + (6 + 26v - 169)x + (9 + 20v - 100) = 0.