Hi Melody.
ok then, Hi Ginger :))
Keep your pantyhose on. I wrote it down somewhere just in case this ever happened.
You have 3 minutes. Then I'm gone.
I'm going to drink this myself and then log off. It’s starting to melt..
I’m trying to remember my password.
Well . . . . .!!
OH no, I’m the one who’s waiting. You log on then I serve you your daiquiri.
Well I’m waiting . . . .what's the hold up?
All my daiquiris are no peal and no spit, except for the special, old-fashioned ones that I make for Lancelot.
You shouldn’t jump to conclusions, JB. At your age, you shouldn’t be jumping at all.
Anyway, just because someone likes one of your posts doesn’t mean that person is a fan.
Great. No peal and no spit.
I have a good idea who one of my fans might be. Hectictar was the only other one on when I got that point. So . . . .
Done. I’ll start making it now.
I’ll let your fans introduce themselves.
Oh, we are in top form tonight . . .
OK I thought about it. I will, but I want one of your famous banana daiquiris.
Who are the others who like my posts?
Good! You do that. Don’t think too hard, you might overheat your brain.
Well, yes, but looks aren’t everything. Anyway, there’s not exactly a lot of competition on here, but yes, I do. I’m not the only either.
No. the point wasn't from me.
Yeah. Well I broke my computer. I have to reboot every 3 or 4 refreshes, because it hangs.
I’ll think about it.
Do you really think I am that funny?
I see someone gave me a point, was that you?
I broke the thread
.
Jesus, JB what do you want to hide for? This forum has some great mathematicians, but it lacks humorous and articulate trolls. You are the funniest troll on here since Lancelot Link and Nauseated, (besides moi, of course). Quit hiding under your bridge! Come out and play. You can always go back to hiding, when you have a mind to.
Hmmm . . . Maybe she was his secretary before she married him.
Really? I thought it was his thirteen-year-old wife, who did that after she tired of taking his dictation. Smart girl!
ROFLMFAO! It depended on the boss whether or not I’d sit in his lap. If he was a hunk and not too frisky I might sit in his lap. As for coffee, one thing none of them liked was having it dumped in their lap. Rumor has it that Jerry Lee Lewis wrote his famous song, Great Balls of Fire, after his secretary dumped hot coffee in his lap.
Suppose that for some a,b,c we have
a+b+c = 6,
ab + ac + bc = 5, and
abc = -12.
What is a^3 + b^3 + c^3?
1.
\(\small{ \begin{array}{|rcll|} \hline (a+b+c)\times (ab + ac + bc) &=& 6\cdot 5 \\ (a+b+c)\times (ab + ac + bc) &=& 30 \\ a^2b+a^2c+abc+ab^2+abc+b^2c+abc+ac^2+bc^2 &=& 30 \\ a^2(b+c) +b^2(a+c) +c^2(a+b)+ 3abc &=& 30 \\ a^2(b+c) +b^2(a+c) +c^2(a+b) &=& 30 - 3abc \quad & | \quad abc = -12 \\ a^2(b+c) +b^2(a+c) +c^2(a+b) &=& 30 - 3(-12) \\ a^2(b+c) +b^2(a+c) +c^2(a+b) &=& 30 +36 \\ \mathbf{a^2(b+c) +b^2(a+c) +c^2(a+b)} & \mathbf{=} &\mathbf{66} \\ \hline \end{array} }\)
2.
\(\small{ \begin{array}{|rcll|} \hline (a+b+c)^3 &=& (a+b+c)^2\times (a+b+c) \\ 6^3 &=& \Big(a^2+b^2+c^2+2(ab + ac + bc ) \Big)\times (a+b+c) \quad | \quad ab + ac + bc = 5 \\ 216 &=& (a^2+b^2+c^2+2\cdot 5 )\times (a+b+c) \\ 216 &=&(a^2+b^2+c^2+10 )\times (a+b+c) \\ 216 &=&a^3+a^2(b+c)+b^3+b^2(a+c)+c^3+c^2(a+b)+10(a+b+c) \\ 216 &=&a^3+b^3+c^3+a^2(b+c)+b^2(a+c)+c^2(a+b)+10(a+b+c) \quad | \quad a+b+c = 6\\ 216 &=&a^3+b^3+c^3+a^2(b+c)+b^2(a+c)+c^2(a+b)+10\cdot 6\\ 216 &=&a^3+b^3+c^3+a^2(b+c)+b^2(a+c)+c^2(a+b)+60 \\ 216-60 &=&a^3+b^3+c^3+a^2(b+c)+b^2(a+c)+c^2(a+b)\\ 156 &=&a^3+b^3+c^3+\underbrace{a^2(b+c)+b^2(a+c)+c^2(a+b)}_{=66} \\ 156 &=&a^3+b^3+c^3+66 \\ 156-66 &=&a^3+b^3+c^3 \\ 90 &=&a^3+b^3+c^3 \\ \mathbf{a^3+b^3+c^3} & \mathbf{=} &\mathbf{90} \\ \hline \end{array} }\)
