I need to solve this inequality:
3(x-1)^2 > 0
The answer is x �‚ 1, but I don't understand why the answer is not allowed to be equal to 1?
Thanks :)
3 answers
Sorry, the symbol did not come out properly when I posted the question. The answer to the question is x followed by an equals sign with a line going through it then 1.
Look at the expression
(x-1)^2
When you square anything, the result is always positive unless you squared zero, which would stay at zero.
3(x-1)^2 > 0
divide by +3
(x-1)^2 > 0
now for what value is x-1 equal to zero?
x-1 = 0
x = 1
now take any value of x you want, positive or negative, take 1 away and square you will always get a positive answer.
EXCEPT, when x = 1, we get 0^2 > 0 which is false, so ....
the solution would be
x ∈ R, x ≠ 1
if your question had been
3(x-1)^2 ≥ 0, then it would include x=1
and x ∈ R
(x-1)^2
When you square anything, the result is always positive unless you squared zero, which would stay at zero.
3(x-1)^2 > 0
divide by +3
(x-1)^2 > 0
now for what value is x-1 equal to zero?
x-1 = 0
x = 1
now take any value of x you want, positive or negative, take 1 away and square you will always get a positive answer.
EXCEPT, when x = 1, we get 0^2 > 0 which is false, so ....
the solution would be
x ∈ R, x ≠ 1
if your question had been
3(x-1)^2 ≥ 0, then it would include x=1
and x ∈ R
Thank you for answering, it really helped :)
Just wondering when I am supposed to know to put x �¸ R?
Thanks
Just wondering when I am supposed to know to put x �¸ R?
Thanks