Zero Sum Numbers Identity Explained
Let the three numbers be represented by $a$, $b$, and $c$. The question states that the sum of these three numbers is zero:
$a + b + c = 0$
We need to find the value of the sum of their cubes, which is $a^3 + b^3 + c^3$. There is a standard algebraic identity:
If $a + b + c = 0$, then $a^3 + b^3 + c^3 = 3abc$
This identity directly shows the relationship when the sum of three numbers is zero. The sum of the cubes ($a^3 + b^3 + c^3$) is equal to three times the product of the numbers ($3abc$).
Therefore, the correct option is the one that states 'three times the product of the three numbers'.
Similar Questions
- If $x + \frac{1}{x} = 2$, then the value of $x^{2} + \frac{1}{x^{2}} = ?$
- If $x + y + z = 0$, then what will be the value of $\frac{x^2}{yz} + \frac{y^2}{zx} + \frac{z^2}{xy}$ ?
- If $x^3 + \frac{1}{x^3} = 18$, then what will be the value of $x + \frac{1}{x}$?
- If $x^2 = y+z, y^2 = z+x$ and $z^2 = x+y$, then find the value of $\frac{1}{x+1} + \frac{1}{y+1} + \frac{1}{z+1}$.
- If $x - \frac{1}{x} = 5$, find the value of $x^4 + \frac{1}{x^4}$.
- If $x^4 + \frac{1}{x^4} = 322$ and $x > 1$, then what is the value of $x^3 - \frac{1}{x^3}$?
- 1200 apples were distributed among a group of boys. Each boy got thrice many of the apples as the number of boys in that group. The number of boys in the group was:
- If $x + \frac{1}{x} = 4$, then find the value of $x^2 + \frac{1}{x^2}$
- If $3a + 4b = 2$ and $ab = \frac{1}{36}$, then $27a^3 + 64b^3$ is:
- If $a^2 + b^2 + c^2 + 3 = 2(a + b + c)$, then the value of $(a + b + c)$ is:
Important Questions from Algebra
In the given question, two equations numbered l and II are given. Solve both the equations and mark the appropriate answer.
I. x2 – 26x + 165 = 0
II. y2 – 38y + 357 = 0
Factorize the following:
(x 2- 6xy + 9y 2) - 25
If P and Q are the points on the line Joining A(-2, 5) and B(3, 1) such that
AP = PQ = QB, then the mid point of PQ is
If a number and its reciprocal added it becomes 6, then what will be sum of its square and square of its reciprocal?
If 3x + 2y = 15, and xy = 6. Find the value of (3x3/2) + (4y3/9).
