Algebra and Applications Test 1

Question : 24 of 40

Marks: +1, -0

If x = a - b, y = b - c, z = c - a, then the numerical value of the algebraic expression

x ^3 + y^ 3 + z ^3 - 3xyz

will be:

Solution:

We know the identity

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

Now x = a - b
y = b - c
z = c - a
Adding these equation, we get:
x + y + z = a - b + b - c + c - a
x + y + z = 0
if x + y + z = 0
then

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

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