Question

When solving a radical equation, Beth and Kelly came to two different conclusions. Beth found a solution, while Kelly's solution did not work in the equation.

Create and justify two situations: one situation where Beth is correct and a separate situation where Kelly is correct.

Answer 1

Will medal! I need this done tonight

Answer 2

some radical equations have no solution

Answer 3

here is an example of a radical equation that has no solution

sqrt( x + 3) = -1

Answer 4

here is a radical equation that has a solution
sqrt( x + 3) = 2

Answer 5

sqrt(x)=-3
if squared both sides x=9
and if check sqrt(9)=-3 ?
3=-3?!

Answer 6

yes thats a simpler example

Answer 7

The equation
sqrt(x) = 3 does have a solution:

if you square both sides you get
x = 3^2 =9
Check:
sqrt(9) = 3

sqrt(x) = -3 does not have a solution
if you square both sides you get
x = (-3)^2 = 9

Check:
sqrt(9) = 3 , not -3

Answer 8

so solving a radical equation by squaring does not necessarily produce a solution. sometimes we get what is called 'extraneous solution'

Answer 9

ok