Solution:
Given:a+b+c=0
We know that ,
a³+b³+c³−3abc
=(a+b+c)(a²+b²+c² −bc−ca−ab)
Put the given value we get:
a³+b³+c³−3abc
=0×(a²+b²+c²−bc−ca−ab)
∴a³+b³+c³−3abc=0
∴a³+b³+c³=3abc.
So option A)3abc is the correct answer.
MathematicsIf a+b+c=0then a³+b³+c³ is equal toGrade : 9
If a+b+c=0then a³+b³+c³ is equal to
Grade : 9
a+b+c=0
We know that ,
a³+b³+c³−3abc
=(a+b+c)(a²+b²+c² −bc−ca−ab)
Put the given value we get:
a³+b³+c³−3abc
=0×(a²+b²+c²−bc−ca−ab)
∴a³+b³+c³−3abc=0
∴a³+b³+c³=3abc.
So option A)3abc is the correct answer.
