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

Options

A. `1/sqrt2`
B. `sqrt2`
C. 2
D. `1/2`

Answer

B

Explanation

Let x=p+q Then
`x=p+sqrt(1-p^2)`
`rArr(dx)/(dp)=1-p(1-p^2)^(-1//2) and (d^2x)/(dp^2)=1/((1-p^2)^(3//2))`
`therefore (dx)/(dp)=0rArrp=1/sqrt 2`
clearly, `(d^2x)/(dp^2)lt0 " for "p=1/sqrt 2`
`"For " P=1/(sqrt2), " we get " q=1/sqrt2 " " [thereforep^2+q^2=1]`
`therefore p+q=sqrt2`