If x+y+z=0, show that x 3 +y 3 +z 3 = 3xyz.

It is known that, \(\overline{x^3 + y^3 + z^3 - 3xyz} =\overline{ (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)}\) put x + y + z = 0, x 3 + y 3 + z 3 - 3xyz = (0) (x 2 + y2 + z 2 - xy - yz - zx) = x 3 + y 3 + z 3 - 3xyz = 0 = x 3 + y 3 + z 3 = 3xyz

Question:

If x+y+z=0, show that x³+y³+z³= 3xyz.

CBSE Class IX

Updated On: Nov 18, 2023

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Solution and Explanation

It is known that,

\(\overline{x^3 + y^3 + z^3 - 3xyz} =\overline{ (x + y + z)(x^2 + y^2 + z^2 - xy - yz - zx)}\)
put x + y + z = 0,
x³ + y³ + z³ - 3xyz = (0) (x²+ y2 + z² - xy - yz - zx)

= x³ + y³ + z³ - 3xyz = 0

= x³ + y³ + z³ = 3xyz

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If x+y+z=0, show that x3+y3+z3= 3xyz.

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Questions Asked in CBSE Class IX exam

If x+y+z=0, show that x³+y³+z³= 3xyz.