If `x+a=y+b+1=z+c` then the value of `[[x, (a+y), (a+x)], [y, (b+y), (b+y)], [z, (c+y), (c+z)]]` is

If a=x-y,b=y-z and c=z-x then the value of a^(3)+b^(3)+c^(3)

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

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

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

If (x)/(b + c - a) = (y)/(c + a - b) = (z)/(a + b - c) , then value of x(b -c) + y(c -a) + z(a - b) is equal to

If the system of equation x=a(y+z),y=b(z+x),z=c(x+y),(a,b,c!=-1) has a non-zero solution then the value of (a)/(a+1)+(b)/(b+1)+(c)/(c+1) is

If a + x = b + y = c + z + 1 , where a, b,c,x,y,z are non polar distinct real numbers , then |(x, a+y,x + a),(y , b+y , y + b),(z,c+y, z+c)| is equal to :

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