Show the following expressions are not equivalent in two different ways

Question

12 + X and √144 + X^2

Answer 1

assume they are equal

12+x=√144+x²

12+x=12+x²

12-12+x=12-12+x²

x=x²

x²-x=0

x(x-1)=0

x=0, or

x-1=0 and x=1

they are equivalent only for x=0 and x=1

to be equivalent they must be equal for all real numbers, not just two

 

Answer 2

1.  the square  root of 144 can be equal to either 12 or -12.  If sqrt 144 = -12, the two equations would not be equivalent.  unless x = positive 1,  and sqrt 144 is equal only to positive 12, the two equations could not be equivalent.