Meehan98
  • Meehan98
Identify a counterexample to disprove n3 ≤ 3n^2, where n is a real number. n = 2 n = −1 n = 0 n = 0.5
Mathematics
katieb
  • katieb
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Meehan98
  • Meehan98
It's supposed to be n^3 < or equal to 3n^2.
MrNood
  • MrNood
just put the 4 values into the inequality only one of them gives an incorrect result - but that proves the inequality is not true for all real numbers, as required
Meehan98
  • Meehan98
I did that and I got; 8<12=true -1<3=true 0=0=true .25<.75=false

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Meehan98
  • Meehan98
So, it would be 0.5 but that's incorrect.
MrNood
  • MrNood
0.5 ^3 is not 0.25
MrNood
  • MrNood
however 0.125 <=0.75 so I believe 0.5 IS the correct answer
Meehan98
  • Meehan98
Okay, the computer must be incorrect then.
MrNood
  • MrNood
hold on a minute tho sorry...
MrNood
  • MrNood
0.5^3 =.125 so the inequality IS true but it is also true for all the other answers
MrNood
  • MrNood
if x>3 then the inequality is false - but that is not an option did oyu type the question correctly?
Meehan98
  • Meehan98
This is a screenshot of the exact problem, and the red arrow means that's the answer I picked and it was incorrect.
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MrNood
  • MrNood
yeah - as I corrected myself - ALL the answers seem to give a correct solution to the inequality - so none is a 'counterexample' any value x>3 IS a counterexample
Meehan98
  • Meehan98
hmm.. okay. Thank you.

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