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If x+y+z=0,show that x^3 + y^3 …

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

Posted by Vyapak Soni 6 years, 7 months ago

CBSE > Class 09 > Mathematics

1 answers

Yogita Ingle 6 years, 7 months ago

If x+y+z=0, show that x³ + y³ + z³= 3xyz
Given that :
x + y + z = 0 ......(1)
We know that,
x³ + y³ + z³ - 3xyz =(x + y + z)(x² + y² + z² - xy - yz - zx) ......(2)
Substituting the value of (1) in (2), we get
x³ + y³+ z³ - 3xyz = 0
x³+ y³ + z³ = 3xyz

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CBSE > Class 09 > Mathematics