If a + b + c = 0, then the value of a 3 + b 3 + c 3 is 1. 0 2. abc 3. 2abc 4. 3abc

We know that, a 3 + b 3 + c 3 - 3abc = (a + b + c)(a 2 + b 2 + c 2 - bc - ca - ab). Substituting values we get, a 3 + b 3 + c 3 - 3abc = 0 × (a 2 + b 2 + c 2 - bc - ca - ab) a 3 + b 3 + c 3 - 3abc = 0 a 3 + b 3 + c 3 = 3abc. Hence, Option 4 is the correct option.

Mathematics

If a + b + c = 0, then the value of a³ + b³ + c³ is
0
abc
2abc
3abc

Expansions

8 Likes

Answer

We know that,

a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - bc - ca - ab).

Substituting values we get,

a³ + b³ + c³ - 3abc = 0 × (a² + b² + c² - bc - ca - ab)

a³ + b³ + c³ - 3abc = 0

a³ + b³ + c³ = 3abc.

Hence, Option 4 is the correct option.

Answered By

4 Likes

Mathematics

If a + b + c = 0, then the value of a³ + b³ + c³ is
0
abc
2abc
3abc

Expansions

Answer

Related Questions

The value of 249² - 248² is
1²
477
487
497

Mathematics

If a + b + c = 0, then the value of a3 + b3 + c3 is0abc2abc3abc

Expansions

Answer

Related Questions

The value of 2492 - 2482 is12477487497

Consider the following two statements :Statement 1: If a + b = 0, then a2 + b2 = 0Statement 2: a2 + b2 = (a + b)2.Which of the following is valid?Both the statements are true.Both the statements are false.Statement 1 is true, and Statement 2 is false.Statement 1 is false, and Statement 2 is true.

If a + b + c = 0, then the value of a³ + b³ + c³ is
0
abc
2abc
3abc

The value of 249² - 248² is
1²
477
487
497