Re: ISI 2013 ME - I Answer Key

Posted by wolverine on May 01, 2013; 8:41pm
URL: http://discussion-forum.276.s1.nabble.com/ISI-2013-ME-I-Answer-Key-tp7579715p7580309.html

13)
A.M.>=G.M
for a and b

((a+b)/2)^2>= ab
a^2+b^2+2ab>=4ab
a^2+b^2>=2ab.....(1)
similarily
b^2+c^2>=2bc.....(2)
a^2+c^2>=2ac.....(3)

adding 1,2,3,

2(a^2+b^2+c^2)>=2(ab+bc+ac)......(4)

as a^2+b^2+c^2=1....(5)

4 and 5 gives   ab+bc+ca <= 1.........(6)



also (a+b+c)^2>=0         as square of any no is greater than or eqal to zero

a^2+b^2+c^2 + 2(ab+bc+ca) >=0
1+ 2(ab+bc+ca) >=0

(ab+bc+ca) >= -1/2  (7)


6 and 7 gives (ab+bc+ca)  belongs to [-1/2,1]