Minimum value of `(b+c)//a+(c+a)//b+(a+b)//c` (for real positive numbers `a ,b ,c)` is (a)`1` (b)`2` (c)`4` (d)`6`

The minimum value of P=b c x+c a y+a b z , when x y z=a b c , is

If a ,b ,c in R^+ , then the minimum value of a(b^2+c^2)+b(c^2+a^2)+c(a^2+b^2) is equal to (a) a b c (b) 2a b c (c) 3a b c (d) 6a b c

If a , b , c , are positive real numbers, then prove that (2004, 4M) {(1+a)(1+b)(1+c)}^7>7^7a^4b^4c^4

Given a matrix A=[a b c b c a c a b],w h e r ea ,b ,c are real positive numbers a b c=1a n dA^T A=I , then find the value of a^3+b^3+c^3dot

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

If a, b and c are distinct positive numbers, then the expression (a + b - c)(b+ c- a)(c+ a -b)- abc is:

If a , b and c are the side of a triangle, then the minimum value of (2a)/(b+c-a)+(2b)/(c+a-b)+(2c)/(a+b-c)i s (a) 3 (b) 9 (c) 6 (d) 1

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 > -c

If a ,b ,a n dc are positive and a+b+c=6, show that (a+1//b)^2+(b+1//c)^2+(c+1//a)^2geq75//4.

If a ,b ,c ,d in R^+-{1}, then the minimum value of (log)_d a+(log)_b d+(log)_a c+(log)_c b is (a) 4 (b) 2 (c) 1 (d)none of these