CMAT 2015 Solved Question Paper

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Question : 15 of 100

Marks: +1, -0

If

(a^2 + b^2 +c^2)

= 1 ,then what can be the minimum value of (ab + bc + ca)?

0
$1/2$
1
- $1/2$

Solution:

(d) We have,

(a+b+c)^2

=

(a^2 + b^2 +c^2)

+ 2(ab + bc + ca)

\;\;\;\;\;\;\;\;

= 1 + 2(ab + bc + ca)

(a+b+c)^2_{min}

= 0 , where

(a+b+c)^2

≮ 0
⇒ 0 = 1 + 2(ab + bc + ca)
⇒(ab + bc + ca) =

-1/2

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