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

Grimmie

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Please help me solve the exercise:
Find the error in the following argument, sqrt(x^2+1)=x+1 and so let x=2 sqrt(5)=9, therefore 5=9
Thanks in advance!!!
 
Please help me solve the exercise:
Find the error in the following argument, sqrt(x^2+1)=x+1 and so let x=2 sqrt(5)=9, therefore 5=9
Thanks in advance!!!
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?
 
Please help me solve the exercise
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:
 
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"? ;)
 
Please help me solve the exercise:
Find the error in the following argument, sqrt(x^2+1)=x+1 and so let x=2 sqrt(5)=9, therefore 5=9
Thanks in advance!!!
1st of all sqrt(5) is not 5, so even if sqrt(5) = 9 it does NOT follow that 5=9.
You mean to ask how does sqrt(5) = 9?

The equation you wrote is what is called a condition equation. It is only valid for 1 or more x values, if any.

Consider x+3 = 5. If we let x=7, then we get 7+3 = 5 or 10 = 5. This is not true, SO X IS NOT 7.
On the other hand, if we let x=2, then 2+3=5 or 5 = 5 which is true, so X = 2 IS THE CORRECT ANSWER
 
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