Doubt regarding the square of a no. $<2$

Question

For $x<2$ which of the following statement is always true:-

$x$ is negative
$2x \ge x$
$x^2 \ge x$
None of these

Taking examples:- $1$ is false, If $x$ is negative $2$ is false But $3$ is always true So answer must be $3$ But the answer key says that the answer is $4$. Who is correct? If I am wong, please explain.

3 isn't always true. I suggest drawing the graph of $y=x^2-x$ for $x$ between $0$ and $2$. — Angina Seng, Oct 22 '17 at 15:50
Maybe of interest. https://math.stackexchange.com/questions/2481633/how-to-prove-forall-x-x2-gt-x/2481822#2481822 — Peter Szilas, Oct 22 '17 at 16:01

score 0 · Answer 1 · answered Oct 22 '17 at 18:01

0

How you said, 1-2 is true. But taking any $x\in (0,1)$ we have $x^2< x$. Therefore the correct answer is 4.

answered Oct 22 '17 at 18:01

Marcelo

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Doubt regarding the square of a no. $<2$

1 Answers1