2. The equation x+2=√3x+10
is of the form
x+a=√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=√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.
Please all written answers. No pictures... :)