If `a^2+b^2+c^2=x^2+y^2+z^2=1,` then show that `a x+b y+c z<1.`

If a^(x)=b^(y)=c^(z) and b^(2)=ac, then show that y=(2zx)/(z+x)

If (2y + 2z - x)/a = (2z + 2x - y)/b = (2x + 2y - z)/c ,then show that (9x)/(2b + 2c - a) = (9y)/(2c + 2a - b) = (9z)/(2a + 2b - c)

If a, b, c, x, y, z are real and a^(2)+b^(2) + c^(2)=25, x^(2)+y^(2)+z^(2)=36 and ax+by+cz=30 , then (a+b+c)/(x+y+z) is equal to :

If (a^(2)+b^(2)+c^(2))(x^(2)+y^(2)+z^(2))=(ax+by+cz)^(2), then show that x:a=y:b=z:c

If 2b = a + c and y^(2) = xz , then what is x^(b-c) y^(c-a)z^(a-b) equal to ?

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 a^2=by +cz " " b^2=cz+ax and c^2=ax+by , then the value of (x)/(a+x) + (y)/(b+y) +(z)/(c+z) will be

Show that |a b c a+2x b+2y c+2z x y z|=0

if (x)/(a^(2)-b^(2))=(y)/(b^(2)-c^(2))=(z)/(c^(2)-a^(2)) , then prove that x+y+z=0.