-1 DOES work, if you take the (perfectly valid) negative square root of 1 in the original equation.
Both answers are correct
Can someone please tell me if my work and solution looks correct. I am a little unsure of whether or not I did it correctly.
Equation: sqrt(x+2) - x = 0
sqrt(x+2) = x
x + 2 = x^2
x^2 - x - 2 = 0
(x-2)(x+1) = 0
x = 2 and x = -1
-1 does not work, so the answer would be x = 2
8 answers
Thank you!
It looks ok to me.
2 works, but doesn't -1 work also?
sqrt(x+2)=x
sqrt(-1+2)=-1
sqrt(1)=-1
-1 or +1 = -1
2 works, but doesn't -1 work also?
sqrt(x+2)=x
sqrt(-1+2)=-1
sqrt(1)=-1
-1 or +1 = -1
by definition, the √ symbol means to take the positive square root of a number
so when you try to verify x = -1
LS = √(-1+2)-(-1)
= 1 + 1
= 2
which is not equal to RS
to see this, we could graph the corresponding function
f(x) = √(x+2) - x
this function is defined only for x≥-2, and has a single y-intercept of √2 and a single x-intercept of 2
so the only solution is x = 2
so when you try to verify x = -1
LS = √(-1+2)-(-1)
= 1 + 1
= 2
which is not equal to RS
to see this, we could graph the corresponding function
f(x) = √(x+2) - x
this function is defined only for x≥-2, and has a single y-intercept of √2 and a single x-intercept of 2
so the only solution is x = 2
I learn something about math every time I answer one of these questions. I guess that's why I should stick to chemistry questions--but I can't answer all of them either.
<<by definition, the �ã symbol means to take the positive square root of a number>>
Well I'm not a math teacher, but I was never taught that
Well I'm not a math teacher, but I was never taught that
Nor was I in my algebra class of 1943. This COULD be a case of changing the rules (as has been done with all the SI units). A micron isn't a micron anymore (:(]. In fact my algebra teachers said, "DON'T forget there is a negative root of the square root of 4."
Not really changing the rules, more what is meant by terminology. My understanding is that the
principal square root function, Sqrt(x), always returns a positive value by definition (as mentioned above).
However, every positive number x has two square roots
one of which is +Sqrt(x)
and the other is -Sqrt(x).
Does this help?
principal square root function, Sqrt(x), always returns a positive value by definition (as mentioned above).
However, every positive number x has two square roots
one of which is +Sqrt(x)
and the other is -Sqrt(x).
Does this help?