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 product without multiplying directly:
104 × 96
Evaluate the following using identities:
117 x 83
Simplify the following: 175 x 175 x 2 x 175 x 25 x 25 x 25
If 9x2 + 25y2 = 181 and xy = −6, find the value of 3x + 5y
If a + b = 10 and ab = 21, find the value of a3 + b3
Evaluate of the following:
933 − 1073
Simplify of the following:
(x+3)3 + (x−3)3
If `x^4 + 1/x^4 = 194, "find" x^3 + 1/x^3`
If x = −2 and y = 1, by using an identity find the value of the following
If x = −2 and y = 1, by using an identity find the value of the following
If \[3x + \frac{2}{x} = 7\] , then \[\left( 9 x^2 - \frac{4}{x^2} \right) =\]
Use identities to evaluate : (998)2
Evaluate: `(4/7"a"+3/4"b")(4/7"a"-3/4"b")`
Expand the following:
(3x + 4) (2x - 1)
If x + y = 1 and xy = -12; find:
x2 - y2.
If x + y + z = 12 and xy + yz + zx = 27; find x2 + y2 + z2.
Factorise the following:
`(2x + 1/3)^2 - (x - 1/2)^2`
Factorise the following:
9x2 + 4y2 + 16z2 + 12xy – 16yz – 24xz
Factorise the following:
25x2 + 16y2 + 4z2 – 40xy + 16yz – 20xz
