Advertisements
Advertisements
प्रश्न
If 3x − 2y = 11 and xy = 12, find the value of 27x3 − 8y3
Advertisements
उत्तर
In the given problem, we have to find the value of `27x^3 - 8y^3`
Given `3x- 2y= 11,xy = 12`,
In order to find `27x^3 - 8y^3`we are using identity `(a-b)^3 = a^3 - b^3 - 3ab (a-b)`
`(3x - 2y)^3 = (11)^3`
`27x^3 - 8y^3 -3 (3x)(2y)(3x- 2y) = 11 xx 11 xx 11`
`27x^3 - 8y^3 -3 (3x)(2y)(3x- 2y) = 1331`
Here putting, 3x - 2y = 11,xy= 12
`27x^3 - 8y^3 - 18 xx 12 xx 11 = 1331`
`27x^3 -8y^3 - 2376 = 1331`
`27x^3 - 8y^3 = 1331 + 2376`
`27x^3 -8y^3 = 3707`
Hence the value of `27x^3 - 8y^3`is 3707.
APPEARS IN
संबंधित प्रश्न
Expand the following, using suitable identity:
`[1/4a-1/2b+1]^2`
Factorise:
4x2 + 9y2 + 16z2 + 12xy – 24yz – 16xz
Evaluate the following using suitable identity:
(998)3
Factorise the following:
`27p^3-1/216-9/2p^2+1/4p`
Factorise the following:
27y3 + 125z3
Simplify the following
`(7.83 + 7.83 - 1.17 xx 1.17)/6.66`
Simplify the following products:
`(x/2 - 2/5)(2/5 - x/2) - x^2 + 2x`
Simplify the following expressions:
`(x + y - 2z)^2 - x^2 - y^2 - 3z^2 +4xy`
If \[x + \frac{1}{x} = 5\], find the value of \[x^3 + \frac{1}{x^3}\]
Evaluate the following:
(98)3
Find the following product:
If x = 3 and y = − 1, find the values of the following using in identify:
(9y2 − 4x2) (81y4 +36x2y2 + 16x4)
If \[x + \frac{1}{x} = 3\] then \[x^6 + \frac{1}{x^6}\] =
If a + b = 7 and ab = 10; find a - b.
If a - b = 4 and a + b = 6; find
(i) a2 + b2
(ii) ab
If a - `1/a`= 8 and a ≠ 0 find :
(i) `a + 1/a (ii) a^2 - 1/a^2`
If `x + (1)/x = "p", x - (1)/x = "q"`; find the relation between p and q.
Which one of the following is a polynomial?
If a + b + c = 0, then a3 + b3 + c3 is equal to ______.
Find the value of x3 – 8y3 – 36xy – 216, when x = 2y + 6
