If p and q are positive real numbers such that p² + q² = 1, then the maximum value of (p + q) is

2

1/2

$fraction numerator 1 over denominator square root of 2 end fraction$
$square root of 2$

Solution

square root of 2

Using space straight A. straight M. space greater or equal than space straight G. straight M comma fraction numerator straight p squared space plus straight q squared over denominator 2 end fraction space greater or equal than pq rightwards double arrow space pq space less or equal than 1 half left parenthesis straight p plus straight q right parenthesis squared space equals space straight p squared space plus straight q squared space plus 2 pq rightwards double arrow space left parenthesis straight p plus straight q right parenthesis squared space equals straight p squared space plus straight q squared space plus 2 pq rightwards double arrow space straight p plus straight q space less or equal than square root of 2

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