Advertisements
Advertisements
Question
If a − b = 4 and ab = 21, find the value of a3 −b3
Advertisements
Solution
In the given problem, we have to find the value of `a^3 - b^3`
Given `a-b = -4,ab = 21`
We shall use the identity `(a-b)^3 = a^3- b^3 - 3ab(a-b)`
Here putting, a-b = - 4,ab = 21,
`(4)^3 = a^3 - b^3 - 3 (21) (4)`
`64 = a^3 - b^3 - 252`
`64 + 252 = a^3 -b^3`
`316 = a^3 - b^3`
Hence the value of `a^3 -b^3` is 316.
APPEARS IN
RELATED QUESTIONS
Evaluate the following using suitable identity:
(998)3
Give possible expression for the length and breadth of the following rectangle, in which their area are given:
| Area : 25a2 – 35a + 12 |
If 2x + 3y = 8 and xy = 2 find the value of `4x^2 + 9y^2`
Write in the expanded form: `(x/y + y/z + z/x)^2`
Simplify `(x^2 + y^2 - z)^2 - (x^2 - y^2 + z^2)^2`
If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + bc + ca.
If a + b = 10 and ab = 21, find the value of a3 + b3
Evaluate of the following:
(598)3
Evaluate of the following:
463+343
Simplify of the following:
(x+3)3 + (x−3)3
Simplify of the following:
(2x − 5y)3 − (2x + 5y)3
If \[x^4 + \frac{1}{x^4} = 119\] , find the value of \[x^3 - \frac{1}{x^3}\]
If x + y + z = 8 and xy +yz +zx = 20, find the value of x3 + y3 + z3 −3xyz
If \[x^2 + \frac{1}{x^2} = 102\], then \[x - \frac{1}{x}\] =
If a2 + b2 + c2 − ab − bc − ca =0, then
If a + `1/a`= 6 and a ≠ 0 find :
(i) `a - 1/a (ii) a^2 - 1/a^2`
Use the direct method to evaluate :
(x+1) (x−1)
Simplify by using formula :
(2x + 3y) (2x - 3y)
If m - n = 0.9 and mn = 0.36, find:
m + n
Factorise the following:
16x2 + 4y2 + 9z2 – 16xy – 12yz + 24xz
