Question

if x=y-z show that x³-y³+z³+3xyz​

Answer 1

Answer:

Step-by-step explanation:

In order to prove this ,

Let us use the formula :

x3 + y3 + z3 - 3xyz = ( x + y + z) (x2 + y2 + z2 - xy - yz - xz)

Now let us keep x + y + z = 0

So,

x3 + y3 + z3 - 3xyz = 0

x3 + y3 + z3 = 3xyz

H€nc€ Prov€d...

or

We know that

x^3+y^3+z^3-3xyz=(x+y+z) (x^2+y^2+z^2-xy-yz-zx)

putting x+y+z=0

x^3+y^3+z^3-3xyz=(0) ( x^2+y^2+z^2-xy-yz-zx)

x^3+y^3+z^3=0

x^3+y^3+z^3=3xyz

Hence proved