If `x/(a)=y/(b)=z/(c)` show that `x^(3)/(a^(3))+y^(3)/(b^(3))+z^(3)/(c^(3))=(3xyz)/(abc)`

If x/a=y/b=z/c, then show that (x^3+a^3)/(x^2+a^2)+(y^3+b^3)/(y^2+b^2)+(z^3+c^3)/(z^2+c^2)=((x+y+z)^3+(a+b+c)^2)/((x+y+z)^2+(a+b+c)^2).

If x+y+z=xyz , prove that: a) (3x-x^(3))/(1-3x^(2))+(3y-y^(3))/(1-3y^(2))+(3z-z^(3))/(1-3z^(2))= (3x-x^(3))/(1-3x^(2)).(3y-y^(3))/(1-3y^(2)).(3z-z^(3))/(1-3z^(2)) b) (x+y)/(1-xy) + (y+z)/(1-yz)+(z+x)/(1-zx)= (x+y)/(1-xy) .(y+z)/(1-yz).(z+x)/(1-zx)

Which of the following line is passing through point of intersection of line (x-4)/(2)=(y-3)/(2)=(z-5)/(1) and the plane x+y+z=2 (a) (x)/(2)=(y+1)/(3)=(z-3)/(4) (b) (x-2)/(3)=(y-1)/(3)=(z-3)/(2) (c) (x)/(2)=(y+1)/(3)=(z-2)/(4) (d) (x-2)/(2)=(y+1)/(3)=(z+3)/(4)

If x+y+z=0 show that x^3+y^3+z^3=3x y z .

If a statement is true for all the values of the variable, such statements are called as identities. Some basic identities are : (1) (a+b)^(2)=a^(2)+2ab+b^(2)=(a-b)^(2)+4ab (3) a^(2)-b^(2)=(a+b)(a-b) (4) (a+b)^(3)=a^(3)+b^(3)+3ab(a+b) (6) a^(3)+b^(3)=(a+b)^(3)=3ab(a+b)=(a+b) (a^(2)-ab) (8) (a+b+c)^(2)=a^(2)+b^(2)+c^(2)+2ab+2bc+2ca=a^(2)+b^(2)+c^(2)+2abc((1)/(a)+(1)/(b)+(1)/(c)) (10) a^(3)+b^(3)+c^(3)-3abc=(a+b+c)(a^(2)+b^(2)+c^(2)-ab-bc-ca) =1/2(a+b+c)[(a-b)^(2)+(b-c)^(2)+(c-a)^(2)] If a+b+c=0,thena^(3)+b^(3)+c^(3)=3abc If x,y, z are different real umbers and (1)/((x-y)^(2))+(1)/((y-z)^(2))+(1)/((z-x)^(2))=((1)/(x-y)+(1)/(y-z)+(1)/(z-x))^2+lamda then the value of lamda is

Find the equation of line through (-4, 1,3) & parallel to the plane x+y+z=3 while the line intersects another line whose eqution is x+y-z=x+2y-3z+5 (a) (x+4)/(-3)=(y-1)/(-2)=(z-3)/(1) (b) (x+4)/(1)=(y-1)/(2)=(z-3)/(-3) (c) (x+4)/(-3)=(y-1)/(2)=(z-3)/(1)

Simplify: ((x^(2)-y^(2))^(3) + (y^(2) - z^(2))^(3) + (z^(2) -x^(2))^(3))/((x-y)^(3) + (y-z)^(3) + (z-x)^(3))

If x= a + b, y= a omega^(2) + b omega, z= a omega + b omega^(2) , then show that x^(3)+ y^(3) + z^(3)= 3(a^(3) + b^(3))

Show that: ((a^(x+1))/(a^(y+1)))^(x+y)\ ((a^(y+2))/(a^(z+2)))^(y+z)\ ((a^(z+3))/(a^(x+3)))^(z+x)=1