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let w=e^{(i*pie)/3} and a,b,c,x,y,z be non zero complex numbers such that a+b+c=x a+bw+cw^2=y a+bw^2+cw=z thn the value of ([x]^2+[y]^2+[z]^2)/([a]^2+[b]^2+[c]^2) is??? where [q] is mod q...

Mathematics
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question from iit 2011
ohkay
w is cube root of unity i believe.. the complex cube root of unity

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Other answers:

What's iit?
yeah it is
IIT-indian institute of technology
it is the best institute in india for engineering
Ok, thks, I didn't know...
Not really an engineering question:-)
yeah but after 12 th we have to give entrance test jee( i don't know the full form) it's from that
i had solved the ques using a short cut to save time
jee to get into iit
jee-joint entrance exam
Mind u, maybe u have to be an engineer to solve it..
oh well let me try it well i get confused jee e for entrance or engineering lol
just take a=b=c=1 and get x,y,z and ur done!!!!! lol!!!! but now i want the technical answer
well 3a = x+y+z
that did get me 4 marks in the paper..substitution
right add all the three. 1+w+wsquare is 0
any suggestions estudier??? ishaan i cant find a way ahead of it..
me too but wait a minute
I don't like this kind of problems..:-
well |3a| = |x + y+z|
dude do u remeber (a+b+c)(a+bw+cw^2)(a+bw^2+cw)=?????? its a formula.. i am not remembering
but x^2 makes the possible minus vanish and hence |x^2 + y^2+x^2| = x^2 + y^2 + z^2 \ just wait like 20 sec
a^2 + b^2 +c^2 -ab +ac -cb
not including (a+b+c)
-ac dude.. all signs were same no?
well including a+b+c it becomes x^3 + y^3 +z^3 -3xyz x=a y=b z=c
ya right.. that was d formula..
lets do it x^2 + y^2 +z^2 you find y while i find x^2 and z^2
ok.. but i believe it is not so lenthy dude.. we get jus 3 minutes for a problem.. there must be some trick
your right
hey (x + y+z) ^2 = x2 +y2 + z2 +2xy + 2xz+2yz
x + y +z = 3a
hey (x + y+z) ^2 = x2 +y2 + z2 +2xy + 2xz+2yz I saw that in your puzzle from yesterday...
9a^2 = x^2 + y^2 +z^2 +2xy + 2zy +2xz
yeah
right
so ^2 make minus sign vanish
it implies x^2 = |x|^2
ofcourse.. its given just to confuse mod is not needed
-ve sign don't exist in squares
letme solve a lil
:D
i believe iit didnt want us to use the substitution method.... coz i have not found a way out till now after 3 months i gae the exam
@face give it a try
damn iit never let someone enter easily
but the substitution method is alays there!!!!! lol!! the only weak point of iit jee.. lol!!!
well what was the options
*always
lol
its an integer type ques 0 to 9 all options
aahhhh scary
generally we mark 2 if we dun kno... 40 percent of ques hav ans 2 lol!!!
Ok , Here I go
ya go go bye. lol js kidding
Okay Here we Have \[x = a+b+c\] \[y =a+bw+cw^2\] \[z = a + bw^2+cw\] Now we have to find \[\large{\frac{|x|^2 + |y|^2 + |z|^2 }{a^2 + b^2 +c^2}}\] \[|z|^2 = z*(conj.z)\] \[conj.y = a+bw^2 +cw\] \[conj.z = a+bw+cw^2\] Okay So we have now \[\frac{(a+b+c)^2 + 2(a + bw+cw^2)(a+bw^2+cw)}{a^2+b^2+c^2}\] \[\frac{3(a^2+b^2+c^2) +2(ab+bc+ac) - 2(ab+bc+ac)}{a^2+b^2+c^2}\]\[3\] Beautiful Solution : )
Beauty

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