Symbiosis National Aptitude Test SNAP 2017 Paper

Question : 24 of 150

Marks: +1, -0

If a, b and c are distinct positive real numbers and

a^2 + b^2 + c^2

= 1, then ab + bc + ca is

Solution:

Since a and bare unequal,

{a^2+b^2}/2

√{a^2b^2}

(A.M. > GM. for unequal numbers)
⇒

a^2 + b^2

> 2ab
Similarly

b^2 + c^2

> 2 be and

c^2 + a^2

> 2ca
Hence

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

> 2 (ab + be + ca)
⇒ ab + bc + ca< 1

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