If `|(a,y,z),(x,b,z),(x,y,c)|=0`, then prove that `(a)/(a-x)+(b)/(b-y)+(c)/(c-z)=2`

If (y/z)^a (z/x)^b (x/y)^c=1 , then prove that (y/z)^((1)/(b-c))=(z/x)^((1)/(c-a))=(x/y)^((1)/(a-b)) .

a^(x)=b^(y)=c^(z) and b^(2)=ac then prove that (1)/(x)+(1)/(z)=(2)/(y)

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

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

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

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

If x=b-c+a, y=c-a+b, z=a-b+c , then prove that (b-a) x + (c-b)y +(a-c)z=0

a(y+z)=x,b(z+x)=y,c(x+y)=z prove that (x^(2))/(a(1-bc))=(y^(2))/(b(1-ca))=(z^(2))/(c(1-ab))

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

If a^(x)=b^(y)=c^(z) and b^(2)=ac prove that (1)/(x)+(1)/(z)=(2)/(y)