When solving a radical equation, John and Tim came to two different conclusions. John found a solution, while Tim's solution did not work in the equation.
Create and justify two situations: one situation where John is correct and a separate situation where Tim is correct.

Question

When solving a radical equation, John and Tim came to two different conclusions. John found a solution, while Tim's solution did not work in the equation.
Create and justify two situations: one situation where John is correct and a separate situation where Tim is correct.

anonymous · Answer

@KirbyLegs could you help me please?

anonymous · Answer

@mathmale could you help me please?

mathmale · Answer

Hi, Maria!
Unusual question!
Let's go with Tim first.  Suppose Tim encounters the radical equation $$\sqrt{x}+9=0.$$
Tim tries to solve this by moving the 9 to the other side of the equation; he subtracts 9 from both sides and obtains $$\sqrt{x}=-9.$$
To eliminate the radical and to solve for x, he now squares both sides of this equation.  Can you help him do that?
What possible solution do the two of you arrive at?
Substitute this possible solution back into the original equation.  Is the resulting equation true or false?
How about you try supervising John.  Guide him in the right direction to create and solve a radical equation whose solution really is a solution, that is, it satisfies the original equation.

anonymous · Answer

it would be false right? because if we substitude 81 it wouldn't give us the answer 0, it would be extraneous right?

mathmale · Answer

Maria:  I'd say Tim's possible solution proved not to be an actual solution to his radical equation, for the reason that the equation is not true when the possible solution (81) is substituted for x in the original (radical) equation.  Not sure I'd call that 81 an "extraneous" solution; better look that up or ask someone else.  Now, are you going to help John out?

anonymous · Answer

i dont know how to help John out? could you help?

mathmale · Answer

Maria:  Tim's case was the more challenging.  Please, experiment:  see whether you can come up with a radical equation that does have a solution.  Look for examples in your book.  Consider changing the one Tim worked on slightly; perhaps that'd be all you'd need to do.

anonymous · Answer

@mathmale you're a fcking bitc-h.

mathmale · Answer

@Nico_dangond :  Sorry you're having a bad day.