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Maths-

General

Easy

Question

If a, b, c are +ve, then $a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent$ is

$> a + b + c$
> ab + bc + ca
< a + b + c
< ab + bc + ca.

The correct answer is: > ab + bc + ca

$fraction numerator a to the power of 2 end exponent plus b to the power of 2 end exponent over denominator 2 end fraction greater than square root of a to the power of 2 end exponent b to the power of 2 end exponent end root$ [ $because$ A.M. > G.M.]
$i. e. a to the power of 2 end exponent plus b to the power of 2 end exponent greater than 2 a b text Similarly end text blank b to the power of 2 end exponent plus c to the power of 2 end exponent greater than 2 b c blank c to the power of 2 end exponent plus a to the power of 2 end exponent greater than 2 c a$
$text Adding end text comma text weget end text 2 open parentheses a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent close parentheses greater than 2 open parentheses a b plus b c plus c a close parentheses i. e. a to the power of 2 end exponent plus b to the power of 2 end exponent plus c to the power of 2 end exponent greater than a b plus b c plus c a.$

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