If a² + b² +c² =ab + bc + ca , then the value of a³+ b³+ c³ is
(a) 3abc
(b)a²b²c²
(c) 3 (abc)³
(d) None of these
Answers
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Answer:
a
3
+ b
3
+ c
3
- 3abc
= (a
2
+ b
2
+ c
2
- ab - bc - ca)(a + b + c)
= a
2
+ b
2
+ c
2
= ab + bc + ca (given)
⇒ (a
2
+ b
2
+ c
2
- ab - bc - ca) = 0
∴ a
3
+ b
3
+ c
3
- 3abc
(a + b + c) x 0 = 0
∴ a
3
+ b
3
+ c
3
= 3abc
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