Do you know algebra?
So it seems that there are some math people around. To follow up on http://www.wallstreetoasis.com/forums/harder-brain... here is another one:
Given:
a^2+b^2=c^2+d^2
a^3+b^3=c^3+d^3
Show that:
a+b=c+d
Requires middle school math, but sure can ruin an interview.
As before, SBs for 1st correct answer.
Edit - all numbers are strictly positive. Apologies for confusion, but the problem remains open.
Edit - To provide an update, this has, thus far, been proven in 1 confirmed way by nonTargetChimp 9 (see his text file proof), and also in 1 more way that appears correct by unForseen (or rather by a friend of unForseen that works in HR). Another proof using trigonometry has been proposed and has not been fully evaluated but could be correct, and blastoise tried to prove this using fancy linear algebra but so far that proof does not appear to be correct, since he was able to prove it ignoring the positive constraint, meaning he proved something that is false. The most elegant solution to date, in my opinion, would have to be the HR rep's as presented by unForseen, which is found on page 8.
Background on the problem - came from an 8th grade city level math competition from the late 1960s at a mathematical school in the USSR.
Just divide the 2nd equation
Just divide the 2nd equation by the first it's really simple.
(a^3 + b^3)/(a^2 + b^2) = (c^3 +d^3)/(c^2+b^2) <=> a+b=c+d
sinthushan wrote: Just divide
Just divide the 2nd equation by the first it's really simple.
(a^3 + b^3)/(a^2 + b^2) = (c^3 +d^3)/(c^2+b^2) <=> a+b=c+d
No such luck.
http://www.wolframalpha.com/input/?i=%28a^3+%2B+b^3%29%2F%28a^2+%2B+b^2%29
I just realized how stupid my
I just realized how stupid my answer was.
sinthushan wrote: Just divide
Just divide the 2nd equation by the first it's really simple.
(a^3 + b^3)/(a^2 + b^2) = (c^3 +d^3)/(c^2+b^2) <=> a+b=c+d
Fail.
Under my tutelage, you will grow from boys to men. From men into gladiators. And from gladiators into SWANSONS.
why can't I just square root
why can't I just square root the 2nd equation? That's whats throwing me off right now. Are you sure the question doesn't ask you to find what a b c d are?
sinthushan wrote: why can't I
why can't I just square root the 2nd equation? That's whats throwing me off right now. Are you sure the question doesn't ask you to find what a b c d are?
You can "square root" a perfect square, only. The question is correct as it is.
Take the square root of each
Take the square root of each variable?
I eat success for breakfast...with skim milk
TonyPerkis wrote: Take the
Take the square root of each variable?
doesn't work that way (a^2 + b^2)^1/2 doesn't equal a+b
Re-write 2nd equation as:
Re-write 2nd equation as:
a^2 . a + b^2 . b = c^2 . c + d^2 . d
then divide it by 1st equation and end up with a+b = c+d ? lol
My guess (disclaimer: I am
My guess (disclaimer: I am not mathematically inclined):
Since we have a ^2 and a ^3, it gives us enough information to eliminate any uncertainty around whether a, b, c, or d is negative or positive. Plug in positive and negative numbers, and you should be able to tell that as long as it satisfies the two equations above, a+b will always equal to c+d.
We wouldn't be able to make that assumption if we were only given a^2 + b^2 = c^2 + d^2, because that tells us nothing about the +/- sign of each number, and you can't safely say a + b = c + d.
Under my tutelage, you will grow from boys to men. From men into gladiators. And from gladiators into SWANSONS.
Flake wrote: My guess
My guess (disclaimer: I am not mathematically inclined):
Since we have a ^2 and a ^3, it gives us enough information to eliminate any uncertainty around whether a, b, c, or d is negative or positive. Plug in positive and negative numbers, and you should be able to tell that as long as it satisfies the two equations above, a+b will always equal to c+d.
We wouldn't be able to make that assumption if we were only given a^2 + b^2 = c^2 + d^2, because that tells us nothing about the +/- sign of each number, and you can't safely say a + b = c + d.
Your intuition may be correct but it is certainly not a proof.
Math Proofs....HUMBUG!!!
Math Proofs....HUMBUG!!!
YOU JUST GOT TROLLED
http://www.troll.me/images/red-foreman322/dont-you...
Dr Joe wrote: Flake
My guess (disclaimer: I am not mathematically inclined):
Since we have a ^2 and a ^3, it gives us enough information to eliminate any uncertainty around whether a, b, c, or d is negative or positive. Plug in positive and negative numbers, and you should be able to tell that as long as it satisfies the two equations above, a+b will always equal to c+d.
We wouldn't be able to make that assumption if we were only given a^2 + b^2 = c^2 + d^2, because that tells us nothing about the +/- sign of each number, and you can't safely say a + b = c + d.
Your intuition may be correct but it is certainly not a proof.
I fail as well.
Under my tutelage, you will grow from boys to men. From men into gladiators. And from gladiators into SWANSONS.
Flake wrote: Dr Joe
My guess (disclaimer: I am not mathematically inclined):
Since we have a ^2 and a ^3, it gives us enough information to eliminate any uncertainty around whether a, b, c, or d is negative or positive. Plug in positive and negative numbers, and you should be able to tell that as long as it satisfies the two equations above, a+b will always equal to c+d.
We wouldn't be able to make that assumption if we were only given a^2 + b^2 = c^2 + d^2, because that tells us nothing about the +/- sign of each number, and you can't safely say a + b = c + d.
Your intuition may be correct but it is certainly not a proof.
I fail as well.
SB for the chuckle
WHOOPS, edited... a^2 + b^2 =
WHOOPS, edited...
a^2 + b^2 = c^2 + d^2
SO
a^2 + b^2 = a^2 + b^2
AND
a^3 + b^3 = a^3 + b^3
THEREFORE
a^x b^x = a^x b^x
SO
a^1 b^1 = a^1 + b^1
AND
a + b = a + b = c + d
a + b = c + d
Or something like that. Apparently, a 5th grader is smarter than me.
YOU JUST GOT TROLLED
http://www.troll.me/images/red-foreman322/dont-you...
Given: a^2+b^2=c^2+d^2 a^3+b^
lookatmycock
Under my tutelage, you will grow from boys to men. From men into gladiators. And from gladiators into SWANSONS.
lookatmycock
Flake wrote: lookatmycock
The above two corrections are
Should I really embarrass
"Look, you're my best friend, so don't take this the wrong way. In twenty years, if you're still livin' here, comin' over to my house to watch the Patriots games, still workin' construction, I'll fuckin' kill you. That's not a threat, that's a fact.
C, let a = 1 b = -1 c = 1 d
Dr Joe wrote: The above two
Will Hunting wrote: Should I
FutureBanker09 wrote: C, let
FutureBanker09 wrote: C, let
Under my tutelage, you will grow from boys to men. From men into gladiators. And from gladiators into SWANSONS.
Dr Joe wrote: FutureBanker09
Will Hunting wrote: Should I
You guys realise that A^3+B^3
somebody go do it the long
Warhead wrote: You guys
FutureBanker09
Will Hunting wrote: Should I
lookatmycock wrote: somebody
Dr Joe wrote: lookatmycock
Let me give it a shot. First,
Just Do It
.
maximumlikelihood wrote: Let
I'm pretty sure for the next
Just Do It
Also, I just showed that if
Just Do It
maximumlikelihood wrote: I'm
I asked a math Phd at
"Look, you're my best friend, so don't take this the wrong way. In twenty years, if you're still livin' here, comin' over to my house to watch the Patriots games, still workin' construction, I'll fuckin' kill you. That's not a threat, that's a fact.
Will Hunting wrote: I asked a
Dr Joe wrote: Will Hunting
"Look, you're my best friend, so don't take this the wrong way. In twenty years, if you're still livin' here, comin' over to my house to watch the Patriots games, still workin' construction, I'll fuckin' kill you. That's not a threat, that's a fact.
Is this doable by direct
does it require using
Warhead wrote: Is this doable
FutureBanker09 wrote: does it
Dr. Joe you're such a tease.
Under my tutelage, you will grow from boys to men. From men into gladiators. And from gladiators into SWANSONS.
This is probably stupid, but