Minimum value of `(x_(1)-x_(2))^(2)+(sqrt(2-x_(1)^(2))+x_(2)-8)^2` ,where `x_(1)in[-sqrt(2),sqrt(2)]` and `x_(2)in R` is

Find the minimum value of (x_1-x_2)^2+(sqrt(2-x_1^2)-9/(x_2))^2 where x_1in(0,sqrt2) and x_2inR^+

Find the minimum value of (x_(1)-x_(2))^(2)+((x_(1)^(2))/(20)-sqrt((17-x_(2))(x_(2)-13)))^(2) where x_(1)in R^(+),x_(2)in(13,17)

(1) x^(2)-(sqrt(2)+1)x+sqrt(2)=0

(1)/(sqrt(2x))+sqrt(2x)

The minimum value of [x_(1)-x_(2))^(2)+(12-sqrt(1-(x_(1))^(2))-sqrt(4x_(2))]^((1)/(2)) for all permissible values of x_(1) and x_(2) is equal to a sqrt(b)-c where a,b,c in N, the find the value of a +b-c

min[(x_(1)-x_(2))^(2)+(3+sqrt(1-x_(1)^(2))-sqrt(4x_(2)))],AA x_(1),x_(2)in R is (a)4sqrt(5)+1 (b) 3-2sqrt(2)(c)sqrt(5)+1(d)sqrt(5)-1

The value of int_(-1)^(1) {sqrt(1+x+x^(2))-sqrt(1-x+x^(2))}dx , is

int(sqrt(1-x^(2))+sqrt(1+x^(2)))/(sqrt(1-x^(2))sqrt(1+x^(2)))dx=

The value of underset(x to 0)lim (sqrt(1+x^(2))-sqrt(1-x^(2)))/(x^(2)) is