Stephanie is student teaching at her local high school. She has to help her instructor write a test. She has to write a radical equation where the solution is extraneous. She also has to write a radical equation where the solution is non-extraneous. Help Stephanie write one radical equation where the solution is extraneous and another equation where the solution is non-extraneous. Using complete sentences, explain each step when solving to justify your examples.

Question

amistre64 · Answer

hint, when we square something, we introduce a possibility for error

anonymous · Answer

I think i am kind of confused about what an extraneous solution is, i tried looking it up but i am still confused.

amistre64 · Answer

extra ... it means that in the process of finding a solution, we introduce the capacity to get something that doesnt fit in the original setup.

amistre64 · Answer

for example:
$$4\sqrt{x}=32$$
when we square something (to undo a sqrt) we introduce a set of solutions that are not a part of the original setup

amistre64 · Answer

in my example, x can only be a value that is 0 or greater

but in the algebra of it all we introduce a negative solution in the process

amistre64 · Answer

spose we have the setup:$$x\sqrt{6}=10$$
in this case we are able to do some algebra without squaring to find x, and thereby we introduce nothing new into the process to worry about

anonymous · Answer

I think I understand it... thanks