The maximum value of `y = sqrt((x-3)^(2)+(x^(2)-2)^(2))-sqrt(x^(2)-(x^(2)-1)^(2))` is
A
3
B
`sqrt(10)`
C
`2sqrt(5)`
D
none of these
Text Solution
Verified by Experts
The correct Answer is:
B
`y = f(x) = sqrt((x^(2)-2)^(2)+(x-3)^(2)) -sqrt(x^(2)+(x^(2)-1)^(2))` Note that the first radical sign describes the distance between `P(x,x^(2))` and `A(3,2)` whereas the second radical sign describes the distance between `P(x,x^(2))` and `B(0,1)`. Now `PA -PB le AB` for possible positions of P. Hence `f(x)]_(max) =` distance between `AB = sqrt(9+1) = sqrt(10)`
