Advertisements
Advertisements
Question
If a − b = −8 and ab = −12, then a3 − b3 =
Options
−244
−240
−224
−260
Advertisements
Solution
To find the value of a3 − b3
Given `a-b = -8,ab =-12`
Using identity `(a-b)^3 = a^3 - b^3 -3ab(a-b)`
Here `a-b = -8,ab =-12`we get
`(-8)^3 = a^3 -b^3 -3ab(a-b)`
`(-8)^3 =a^3 -b^3 -3 xx -12 xx -8`
`-512 = a^3 -b^3 - 288`
Transposing -288 to left hand side we get
`- 512 + 288 = a^3 - b^3`
`-224 = a^3 - b^3`
Hence the value of `a^3 -b^3 `is -224 .
APPEARS IN
RELATED QUESTIONS
Without actually calculating the cubes, find the value of the following:
(28)3 + (–15)3 + (–13)3
Give possible expression for the length and breadth of the following rectangle, in which their area is given:
| Area : 35y2 + 13y – 12 |
Simplify the following:
0.76 x 0.76 - 2 x 0.76 x 0.24 x 0.24 + 0.24
Simplify (a + b + c)2 + (a - b + c)2
Simplify the expression:
`(x + y + z)^2 + (x + y/2 + 2/3)^2 - (x/2 + y/3 + z/4)^2`
If a + b = 10 and ab = 21, find the value of a3 + b3
Simplify of the following:
If x = −2 and y = 1, by using an identity find the value of the following
If \[x + \frac{1}{x} = 3\] then \[x^6 + \frac{1}{x^6}\] =
Evalute : `( 7/8x + 4/5y)^2`
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
Use the direct method to evaluate the following products :
(y + 5)(y – 3)
Use the direct method to evaluate :
(ab+x2) (ab−x2)
Evaluate: `(4/7"a"+3/4"b")(4/7"a"-3/4"b")`
Expand the following:
(x - 3y - 2z)2
If a2 - 3a - 1 = 0 and a ≠ 0, find : `"a"^2 - (1)/"a"^2`
If `"a" + (1)/"a" = 2`, then show that `"a"^2 + (1)/"a"^2 = "a"^3 + (1)/"a"^3 = "a"^4 + (1)/"a"^4`
Factorise the following:
9y2 – 66yz + 121z2
Factorise the following:
9x2 + 4y2 + 16z2 + 12xy – 16yz – 24xz
