If X = 1/2
1/x = 2
2x = 1
x^2 = 1/4
So I works.
If
X = 4/5
1/x = 5/4 = 1.25
2x = 8/5 = 1.6
x^2 = 16/25
So II works.
If X > 1 doesn't work
X = 10
1/x = 1/10
2x = 20
X^2 = 100
X = 1
1,2,1
I would go with I and II only?
Ordering
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KapTeacherEli
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X is positive. That means you can multiply or divide everything by X, to make life easier.
I. divide by x. x < 2 < 1/(x^2)
Pick any small fraction. 1/4 < 2 < 1/(1/16)
II. Divide by x. x < 1/(x^2) < 2
This one is stickier, because we need to keep 1/(x^2) less than two and greater than 1, but 3/4 will do it here; 3/4 < 1/(9/16) < 2
III. Divide again here. 2< x < 1/(x^2)
Impossible. If x is greater than 2, then 1/x will be less than one, and increasing it by a power will make it yet smaller.
Answer is D, I and II only.
I. divide by x. x < 2 < 1/(x^2)
Pick any small fraction. 1/4 < 2 < 1/(1/16)
II. Divide by x. x < 1/(x^2) < 2
This one is stickier, because we need to keep 1/(x^2) less than two and greater than 1, but 3/4 will do it here; 3/4 < 1/(9/16) < 2
III. Divide again here. 2< x < 1/(x^2)
Impossible. If x is greater than 2, then 1/x will be less than one, and increasing it by a power will make it yet smaller.
Answer is D, I and II only.
