Advertisements
Advertisements
Question
Find the value of 27x3 + 8y3, if 3x + 2y = 14 and xy = 8
Advertisements
Solution
In the given problem, we have to find the value of `27x^3 + 8y^3`
Given `3x + 2y = 14, xy = 8`
On cubing both sides we get,
`(3x+ 2y)^3 = (14)^3`
We shall use identity `(a+b)^3 = a^3 + b^3 + 3ab(a+b)`
`27x^3 + 8y^3 + 3(3x) (2y) (3x+ 2y) = 14 xx 14 xx 14`
`27x^3 + 8y^3 +18(xy)(3x+2y) = 14 xx 14 xx 14`
`27x^3 + 8y^3 + 18(8)(14) = 2744`
`27x^3 + 8y^3 + 2016 = 2744`
` 27x^3 + 8y^3 = 2744 -2016`
`27x^3 +8y^3 = 728`
Hence the value of `27x^3 +8y^3`is 728.
APPEARS IN
RELATED QUESTIONS
Factorise the following using appropriate identity:
4y2 – 4y + 1
Write the following cube in expanded form:
`[3/2x+1]^3`
Give possible expression for the length and breadth of the following rectangle, in which their area is given:
| Area : 35y2 + 13y – 12 |
If 9x2 + 25y2 = 181 and xy = −6, find the value of 3x + 5y
Find the cube of the following binomials expression :
\[4 - \frac{1}{3x}\]
If a − b = 4 and ab = 21, find the value of a3 −b3
Find the value of 27x3 + 8y3, if 3x + 2y = 20 and xy = \[\frac{14}{9}\]
Find the following product:
Find the following product:
If \[x + \frac{1}{x} = 3\] then find the value of \[x^6 + \frac{1}{x^6}\].
(a − b)3 + (b − c)3 + (c − a)3 =
Use identities to evaluate : (502)2
Use identities to evaluate : (998)2
Use the direct method to evaluate :
(2a+3) (2a−3)
Find the squares of the following:
9m - 2n
If `"a"^2 - 7"a" + 1` = 0 and a = ≠ 0, find :
`"a"^2 + (1)/"a"^2`
Simplify:
(7a +5b)2 - (7a - 5b)2
Which one of the following is a polynomial?
Simplify (2x – 5y)3 – (2x + 5y)3.
If a + b + c = 5 and ab + bc + ca = 10, then prove that a3 + b3 + c3 – 3abc = – 25.
