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The maximum value of y = sqrt((x-3)^(2...

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)`
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