SOLUTION: What are the (1) roots, and (2) extraneous roots for this equation: x=sqrt(12-x) English: x equals the square root of 12-x Thank you very much.

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: What are the (1) roots, and (2) extraneous roots for this equation: x=sqrt(12-x) English: x equals the square root of 12-x Thank you very much.       Log On


   

Question 1047287: What are the (1) roots, and (2) extraneous roots for this equation:
x=sqrt(12-x) English: x equals the square root of 12-x
Thank you very much.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
You would square both sides and solve the quadratic equation. One of the roots, if there are two of them, will not work. Note that it will NOT WORK IN THE ORIGINAL EQUATION. Look and see that in case you find any x such that x%3C12, this will be wrong for the original equation.

x%5E2=12-x

x%5E2%2Bx-12=0

x=%28-1%2B-+sqrt%281%2B4%2A12%29%29%2F2
x=%28-1%2B-+sqrt%2849%29%29%2F2
x=%28-1%2B-+7%29%2F2
highlight%28system%28cross%28x=-4%29%2Cor%2Cx=3%29%29

Which root is the extraneous root?