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

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

The minimum value of (x^4+y^4+z^2)/(x y z) for positive real numbers x ,y ,z is (a) sqrt(2) (b) 2sqrt(2) (c) 4sqrt(2) (d) 8sqrt(2)

The value of x + y + z is 15. If a, x, y, z, b are in AP while the value of (1)/(x) + (1)/(y) + (1)/(z) " is " (5)/(3) . If a, x, y, z b are in HP, then find a and b .

If x ,ya n dz are in A.P., a x ,b y ,a n dc z in G.P. and a ,b ,c in H.P. then prove that x/z+z/x=a/c+c/a .

Given a=x//(y-z), b=y//(z-x),a n dc=z//(x-y),w h e r ex , y , za n dz are not all zero, then the value of a b+b c+c a is 0 b. 1 c. -1"" d. none of these

In the adjacent figure, find the value of x, y, z and a, b, c.

Find the condition on a, b and c so that the following system of linear equations has one parameter family of solutions: x + y + z = a, x + 2y + 3z = b, 3x + 5y + 7z = c.

Prove that |a x-b y-c z a y+b x c x+a z a y+b x b y-c z-a x b z+c y c x+a z b z+c y c z-a x-b y|=(x^2+y^2+z^2)(a^2+b^2+c^2)(a x+b y+c z)dot

The lines which intersect the skew lines y=m x ,z=c ; y=-m x ,z=-c and the x-axis lie on the surface a. c z=m x y b. x y=c m z c. c y=m x z d. none of these

If in A B C , the distances of the vertices from the orthocentre are x, y, and z, then prove that a/x+b/y+c/z=(a b c)/(x y z)