Advertisements
Advertisements
Question
If a + b + c = 0, then write the value of a3 + b3 + c3.
Advertisements
Solution
Recall the formula
` a^3 + b^3 +c^3 - 3abc = (a+b+c)(a^2 +b^2 +c^2 -ab-bc - ca)`
When (a + b + c) = 0, we have
`a^3 +b^3 +c^3 -3abc = (a^2 +b^2 +c^2 - ab - bc - ca)`
= 0
`a^3 +b^3 +c^3 - 3abc - 0`
⇒ `a^3 +b^3 +c^3 = 3abc`
APPEARS IN
RELATED QUESTIONS
Factorize (x + 2)(x2 + 25) -10x2 - 20x
Factorize `21x^2 - 2x + 1/21`
Find the value of the following expression: 64x2 + 81y2 + 144xy, when x = 11 and \[y = \frac{4}{3}\]
Divide: 9a4b - 15a3b2 + 12a2b3 by - 3a2b
Divide: m3 − 4m2 + m + 6 by m2 − m − 2
Write the coefficient of x2 and x in the following polynomials
`4 + 2/5x^2 - 3x`
If x = 2 and y = 3, then find the value of the following expressions
2x – 3y
If x = 2 and y = 3, then find the value of the following expressions
4y – x
The figure shows the dimensions of a wall having a window and a door of a room. Write an algebraic expression for the area of the wall to be painted.
Match Column I with Column II in the following:
| Column I | Column II |
| 1. The difference of 3 and a number squared | (a) 4 – 2x |
| 2. 5 less than twice a number squared | (b) n2 – 3 |
| 3. Five minus twice the square of a number | (c) 2n2 – 5 |
| 4. Four minus a number multiplied by 2 | (d) 5 – 2n2 |
| 5. Seven times the sum of a number and 1 | (e) 3 – n2 |
| 6. A number squared plus 6 | (f) 2(n + 6) |
| 7. 2 times the sum of a number and 6 | (g) 7(n + 1) |
| 8. Three less than the square of a number | (h) n2 + 6 |
