Prove that the minimum value of `((a+x)(b+x))/((c+x))a ,b > c ,x >-c` is `(sqrt(a-c)+sqrt(b-c))^2`

Show that the minimum value of (x+a)(x+b)/(x+c) wherea >c,b>c is (sqrt(a-c)+sqrt(b-c))^(2) for real values of x>.

If a+b+c=0 , then find the value of sqrt(x^a.x^b.x^c) .

If c!=0 and the equation p/(2x)=a/(x+c)+b/(x-c) has two equal roots,then p can be (sqrt(a)-sqrt(b))^(2) b.(sqrt(a)+sqrt(b))^(2) c.a+b d.a-b

The value of (a-c)/((a-b)(x-a)) + (b-c)/((b-a)(x-b)) is:

The value of (x^(a-b))^(c ) xx (x^(b-c))^(a) xx (x^(c-a))^(b) is

If a,b,c are positive real numbers; then the value of x that minimizes sqrt(a^(2)+x^(2))+sqrt((b-x)^(2)+c^(2))

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