Question

when solving a radical equation john and tim came to 2 different conclusions john found a solution while tim solutions did not fit the equation
Create an justify 2 situations were john is correct and antheir where tim is correct.

Answer 1

@thomaster

Answer 2

\[\sqrt{x}-x=0\]
\[\sqrt{x}=x \rightarrow (\sqrt{x}=x)^2\]
\[x=x^2 \rightarrow x-x^2=0 \rightarrow x(1-x)=0 \rightarrow x=0 , x=1\]
both of roots are correct if check

Answer 3

another
equation with the same idea
\[\sqrt{x}+x=0\]
\[\sqrt{x}=-x \rightarrow (\sqrt{x}=-x)^2\]
\[x=x^2 , x(1-x)=0 \rightarrow x=0 , x=1\]

x=0 is correct
but x=1 is not because sqrt(1)+1=1+1=2 instead of 0