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) where a > c ,b > c , is (sqrt(a-c)+sqrt(b-c))^2 for real values of x > -c .

Show that the minimum value of (x+a)(x+b)//(x+c)dotw h e r ea > c ,b > c , is (sqrt(a-c)+sqrt(b-c))^2 for real values of x >-cdot

Find the minimum value of a x+b y , where x y=c^2 and a ,\ b ,\ c are positive.

If a^2x^4+b^2y^4=c^6, then the maximum value of x y is (c^2)/(sqrt(a b)) (b) (c^3)/(a b) (c^3)/(sqrt(2a b)) (d) (c^3)/(2a b)

If y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/((sqrt(a-x)+sqrt(x-b)) ,then (dy)/(dx) wherever it is defined is (a) (x+(a+b))/(sqrt((a-x)(x-b))) (b) (2x-a-b)/(2sqrt(a-x)sqrt(x-b)) (c) -((a+b))/(2sqrt((a-x)(x-b))) (d) (2x+(a+b))/(2sqrt((a-x)(x-b)))

Prove that the greatest value of x y is c^3/sqrt(2a b) , if a^2x^4+b^2y^4=c^6dot

If a ,b ,c are in A.P., prove that the following are also in A.P. (i) 1/(b c),1/(c a),1/(a b), (ii) b+c ,c+a ,a+b (iii) a(1/b+1/c),b(1/c+1/a),c(1/a+1/b) (iv) a^2(b+c),b^2(c+a),c^2(a+b) (v) 1/(sqrt(b)+sqrt(c)),1/(sqrt(c)+sqrt(a)),1/(sqrt(a)+sqrt(b))

If the line y=mx+c is a tangent to the ellipse x^(2)+2y^(2)=4 , then the minimum possible value of c is (a) -sqrt(2) (b) sqrt(2) (c) 2 (d) 1

Evaluate : sqrt(x^(a-b)) xx sqrt( x^(b-c)) xx sqrt( x^(c-a))

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