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If p and q are positive real numbers such that `p^2+""q^2=""1` , then the maximum value of `(p""+""q)` is (1) 2 (2) 1/2 (3) `1/(sqrt(2))` (4) `sqrt(2)`

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To find the maximum value of \( p + q \) given that \( p^2 + q^2 = 1 \) where \( p \) and \( q \) are positive real numbers, we can use the Cauchy-Schwarz inequality or the method of Lagrange multipliers. Here, we will use the Cauchy-Schwarz inequality for simplicity. ### Step-by-step Solution: 1. **Understanding the constraint**: We know that \( p^2 + q^2 = 1 \). 2. **Using the Cauchy-Schwarz Inequality**: ...
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