"Which of the following equations has no solution(s)?"

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paris567

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Hello, could someone help me with solving this question, i figured and solved all the questions but I'm not sure if I'm 100% right that i know the no solution equations.

my calculations
A. square root of x-3 +5 = 2
2-5
-3
square root of x-3 = -3 (that's as far as i get and than i get no answer)

I believe that A is the only one that has no solution because once you calculate up to \sqrt(x-3)=-3 then i cant get any further and i can't find an answer to the question.
Screen Shot 2021-01-07 at 10.31.15 AM.png
 
You're right for the first one. The "square root function" gives only positive outputs, so it isn't possible for a square root of anything (in this case sqrt(x-3)) to equal -3 < 0. Look up a graph of the square root function, maybe it will be more clear.
But be careful though, the "sqrt function" only works with non-negative numbers as inputs (what is the square root of -1 ?? doesn't exist in the real numbers) so that means that for example in a) x -3 must be >= 0 (for the square root function to be defined). A good way to check this is either set the restriction at the beginning or when you get a solution plug it back in the equation to see what you will get.
 
oh sorry, for square root it is defined in my class: "A square root of a number is a value that, when multiplied by itself, gives the number."
 
paris567 said:
oh sorry, for square root it is defined in my class: "A square root of a number is a value that, when multiplied by itself, gives the number."
Click to expand...
Negative root "when multiplied by itself" would also give you the number. If negative roots are valid then sqrt(x-3)=-3 has solution(s). So, what does your definition say about negative roots?
 
I hope that you are wrong about how square root was defined in class. It should be a square root of a number is a non negative value that when multiplied by itself gives the number.
 
paris567 said:
oh sorry, for square root it is defined in my class: "A square root of a number is a value that, when multiplied by itself, gives the number."
Click to expand...
This is correct when you are talking about A square root (either one of two).

Jomo said:
I hope that you are wrong about how square root was defined in class. It should be a square root of a number is a non negative value that when multiplied by itself gives the number.
Click to expand...
This is correct only if you change "a square root" to "the square root", that is, the symbol [MATH]\sqrt{x}[/MATH].

The square root (radical) is by definition the principal square root, which is the non-negative one.

Now, which one is that equation about? Can the square root there be -3?
 
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