If `V` is the volume of a cuboid of dimensions `x ,\ y ,\ z\ a n d\ A` is its surface area, then `A/V` (a) `x^2y^2z^2` (b) `1/2(1/(x y)+1/(y z)+1/(z x))` (c) `1/2(1/x+1/y+1/z)` (d) `1/(x y z)`

If x , y , z are all different real numbers, then 1/((x-y)^2)+1/((y-z)^2)+1/((z-x)^2)=(1/(x-y)+1/(y-z)+1/(z-x))^2

If x ,y ,z are all different real numbers, then 1/((x-y)^2)+1/((y-z)^2)+1/((z-x)^2)=(1/(x-y)+1/(y-z)+1/(z-x))^2

The value of {(x-y)^3+(y-z)^3+(z-x)^3}/{9(x-y)(y-z)(z-x)} (1) 0 (2) 1/9 (3) 1/3 (4) 1

Prove that : =|{:(1,1,1),(x,y,z),(x^(2),y^(2),z^(2)):}|=(x-y)(y-z)(z-x)

If x+y+z=1,\ x y+y z+z x=-1\ \ a n d\ x y z=-1, find the value of x^3+y^3+z^3

Evaluate each of the following algebraic expressions for x=1,\ y=-1, z=2,\ a=-2,\ b=1,\ c=-2: (i) a x+b y+c z (ii) a x^2+b y^2-c z^2 (iii) a x y+b y z+c x y

If x+y+z=1a n dx ,y ,z are positive, then show that (x+1/x)^2+(y+1/y)^2+(z+1/z)^2>(100)/3

If (1)/(x) , (1)/(y) , (1)/(z) are A.P. show that (y+z)/(x) , (z+x)/(y) , (x+y)/(z) are in A.P.

Perpendiculars are drawn from points on the line (x+2)/2=(y+1)/(-1)=z/3 to the plane x + y + z=3 The feet of perpendiculars lie on the line (a) x/5=(y-1)/8=(z-2)/(-13) (b) x/2=(y-1)/3=(z-2)/(-5) (c) x/4=(y-1)/3=(z-2)/(-7) (d) x/2=(y-1)/(-7)=(z-2)/5

Find all positive real numbers x, y, z such that: 2x-2y + 1/z = 1/(2014), 2y-2z + 1/x = 1/(2014), 2z-2x + 1/y = 1/(2014)