OpenStudy (anonymous):

if x^2 > 0, then x < 0. Is that statement true or false?

5 years ago
OpenStudy (ivettef365):

what do you think ?

5 years ago
OpenStudy (anonymous):

x>0 or x<0

5 years ago
OpenStudy (anonymous):

x<0

5 years ago
OpenStudy (debbieg):

Can you find a counterexample?

5 years ago
OpenStudy (anonymous):

-1

5 years ago
OpenStudy (debbieg):

It says if x^2 > 0, then x < 0. So if you can find an x>0 such that if x^2 > 0, then that DISproves it, hence it is false.

5 years ago
OpenStudy (anonymous):

oh wait. nevermind -1*-1 = 1

5 years ago
OpenStudy (anonymous):

-1 fits the definition... what about something that works in the first part but not the second?

5 years ago
OpenStudy (debbieg):

Note, however, that the reverse is not true: finding an example for which the statement is true does not PROVE that it's true IN GENERAL. But finding an example that proves IT'S FALSE does prove that it's NOT TRUE in genera.

5 years ago
OpenStudy (anonymous):

2

5 years ago
OpenStudy (debbieg):

So what does that tell you? is it true or false?

5 years ago
OpenStudy (anonymous):

Pretty sure it's false. be> 0, or 4 >0, then 4 < 0???

5 years ago
OpenStudy (anonymous):

because 2^2 > 0

5 years ago
OpenStudy (debbieg):

Exactly. :)

5 years ago

What if x has a complex value like 2i ?

5 years ago
OpenStudy (anonymous):

WOOOT THANKS DEBBIE

5 years ago

x = -2, x^2 =4 x =2 , x^2 =4 x=2i, x^2=-4

5 years ago
OpenStudy (anonymous):

just no.

5 years ago
OpenStudy (anonymous):

but which is greater? 2i or -2i? also, is either of these greater or less than 0?

5 years ago
OpenStudy (anonymous):

greater

5 years ago
OpenStudy (anonymous):

can't compare complex numbers... only their moduli!

5 years ago
OpenStudy (anonymous):

so?..

5 years ago

@pgpilot326 Equal but opposite. and when both are squared (-2i)^2 or (2i)^2 the result is still -4 which is less than zero. The drawing shows their relationship to zero, I will let you decide which one is less than or greater than zero :) l|dw:1377641500857:dw|

5 years ago
OpenStudy (anonymous):

1+i or 1 - i?

5 years ago
OpenStudy (anonymous):

besides is 2i >0? if so, is -2i>0? can both be?

5 years ago
OpenStudy (anonymous):

not really?

5 years ago