# Help me find error in argument: sqrt(x^2+1)=x+1; let x=2 sqrt(5)=9, therefore,...

#### Grimmie

##### New member
Find the error in the following argument, sqrt(x^2+1)=x+1 and so let x=2 sqrt(5)=9, therefore 5=9

#### Subhotosh Khan

##### Super Moderator
Staff member
Find the error in the following argument, sqrt(x^2+1)=x+1 and so let x=2 sqrt(5)=9, therefore 5=9
This is clearly a problem involving algebraic equation.

Why are you posting this in pre-algebra section?

How do you know that the given equation [√(x^2 +1) = x + 1] is true?

Is this a Home Work problem? Which grade?

#### mmm4444bot

##### Super Moderator
Staff member
As you've presented it, the exercise is to locate mistake(s) in somebody else's work.

Find the error in the following argument,

sqrt(x^2+1) = x+1

and so let x = 2

sqrt(5) = 9,

therefore 5 = 9
Above, I have highlighted (in red) an error. Focus on that, to start. Once you tell us the correct value, we can discuss the exercise further. :cool:

#### stapel

##### Super Moderator
Staff member
Find the error in the following argument, sqrt(x^2+1)=x+1 and so let x=2 sqrt(5)=9, therefore 5=9
It looks as though you are assuming that sqrt[x^2 + 1] is everywhere (that is, for all values of x) equal to x + 1. Why? You know that (x + 1)^2 is not equal to x^1 + 1 (since powers don't "distribute"), so why are you assuming that the wrong statement "works" "going backwards"?