If p and q are positive real numbers suc...

If `p` and `q` are positive real numbers such that `p^2+q^2=1` then find the maximum value of `(p+q)`

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`P^2+Q^2=1`
`Q^2=1-P^2`
`Q=sqrt(1-P^2)`
`S=P+Q`
`=P+sqrt(1-P^2)`
`(dS)/(dP)=0`
`=1+(1-2P)/(2sqrt(1-p^2))=0`
`=1+(-P)/(sqrt(1-P^2))=0`
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