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What is the value of a3 +b3 +c3,if (a+b+c)=0?
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What is the value of a3 +b3 +c3,if (a+b+c)=0?
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What is the value of a3 +b3 +c3,if (a+b+c)=0?
Given ,(a+b+c)= 0 then ,a+b=-c
cubing both side
(a+b)^3 =-(c)^3
=a^3+b^3+3ab(a+b)=-c^3
=a^3+b^3+3ab×-c = -c^3
=a^3+b^3-3abc = -c^3
=a^3+b^3+c^3 = 3abc(Ans).
cubing both side
(a+b)^3 =-(c)^3
=a^3+b^3+3ab(a+b)=-c^3
=a^3+b^3+3ab×-c = -c^3
=a^3+b^3-3abc = -c^3
=a^3+b^3+c^3 = 3abc(Ans).
Community Answer
What is the value of a3 +b3 +c3,if (a+b+c)=0?
First note that:
a^3 + b^3 + c^3 - 3abc = (a + b + c)(a^2 + b^2 + c^2 - ab - ac - bc).
By assumption a^3+b^3+c^3=3abc so the left hand side is 0.
Therefore (a+b+c)(a^2+b^2+c^2-ab-ac-bc) = 0. So either a+b+c=0 or a^2+b^2+c^2-ab-ac-bc=0.
Now suppose a^2+b^2+c^2 - ab-ac-bc =0. You can re-write this as:
(1/2) ( (a-b)^2 + (b-c)^2 + (c-a)^2 )=0
Therefore (a-b)^2 + (b-c)^2 + (c-a)^2 =0 so a=b=c.
So either a+b+c=0 or a=b=c. (So if a,b,c are all distinct then a+b+c=0).
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What is the value of a3 +b3 +c3,if (a+b+c)=0? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about What is the value of a3 +b3 +c3,if (a+b+c)=0? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the value of a3 +b3 +c3,if (a+b+c)=0?.
What is the value of a3 +b3 +c3,if (a+b+c)=0? for Class 9 2024 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about What is the value of a3 +b3 +c3,if (a+b+c)=0? covers all topics & solutions for Class 9 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the value of a3 +b3 +c3,if (a+b+c)=0?.
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