Published by:
CGP EDU Academic Team
Published on: August 13, 2026
If a, b and c are distinct positive real numbers and a 2 +b 2 +c 2 =1, then ab + bc +ca is
Text Solution
Verified by ExpertsThe correct answer is:
A
Since a and b are unequal, 
(A.M. > G.M. for unequal numbers)
⇒ ⇒ a 2 +b 2 > 2ab.
Similarly b 2 +c 2 > 2bc and c 2 + a 2 > 2ca.
Hence 2(a 2 +b 2 +c 2 ) > 2(ab + bc +ca)
⇒ ⇒ ab + bc + ca < 1.
Hence is the correct answer.
Alternative solution:
It is given that 1 = a 2 + b 2 + c 2
= 
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