Advertisements
Advertisements
प्रश्न
If (x + y)3 − (x − y)3 − 6y(x2 − y2) = ky2, then k =
विकल्प
1
2
4
8
Advertisements
उत्तर
The given equation is
(x + y)3 − (x − y)3 − 6y(x2 − y2) = ky2
Recall the formula
`a^3 - b^3 = (a-b)(a^2 +ab +b^2)`
Using the above formula, we have
`(x+y)^3 - (x-y)^3 - 6y(x^2 -y^2 )ky^2`
`⇒ {(x+y)^3 - (x-y)^3} - 6y (x^2 - y^2) = ky^2`
` ⇒ 2y(x^2 + 2xy + y^2 +x^2 - y^2 - x^2 - 2xy +y^2) -6y(x^2 - y^2) = ky^3`
`⇒ 2y(3x^2 +y^2) -6y(x^2 - y^2) = ky^3`
`⇒6x^2y +2y^3 - 6x^2 y +6y^3 = ky^3`
`⇒ 8y^3 = ky^3`
`⇒ ky^3 = 8y^3`
⇒ k =8, provided y ≠0.
APPEARS IN
संबंधित प्रश्न
Factorize `x^2 + 12/35 x + 1/35`
8x3 + 27y3 - 216z3 + 108xyz
(a – 3b)3 + (3b – c)3 + (c – a)3
Multiply: x2 + y2 + z2 − xy + xz + yz by x + y − z
Evaluate: (c + 5)(c - 3)
Divide: - 16ab2c by 6abc
Divide: 2a2 - 11a + 12 by a - 4
An algebraic statement which is equivalent to the verbal statement “Three times the sum of ‘x’ and ‘y’ is
A school has a rectangular playground with length x and breadth y and a square lawn with side x as shown in the figure given below. What is the total perimeter of both of them combined together?
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 |
