#Is x^2 always larger than x if x(1-x)>0 ?

17 messages · Page 1 of 1 (latest)

merry silo
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My mathbook implies that it is.

But if 0<x<1, doesn't this answer fall apart?

Citations from my book (translated from Swedish):

You receive introductory information followed by two quantities.
Which of the following alternatives are correct?
A: I is larger than II
B: II is larger than I
C: I equals to II
D: Information is insufficient

x(1-x)>0
Quantity I: x
Quantity II: x^2

^ and Im then supposed to answer with either A,B,C or D. My books register says the correct answer is A. I however, believe the correct answer is D as x could be in the range of 0<x<1.

Can somebody explain to me why the correct answer is A?

violet charmBOT
#
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tough cipher
#

We have:
x^2 > x
x^2 - x > 0
x(x - 1) > 0
So, solve this inequality to see where x^2 is larger than x.

versed frigate
merry silo
versed frigate
merry silo
#

Because as written above, my book says that it does (if Ive read it correctly)

tough cipher
#

Well, x(1 - x) > 0 is equivalent to x^2 < x, not x^2 > x.

versed frigate
merry silo
#

oh, now I see

#

I will close this

#

Thank you

#

+close

vale steepleBOT
# merry silo +close
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vale steepleBOT
# vale steeple

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vale steepleBOT
# vale steeple

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