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:
`2x^2 + y^2 + 8z^2 - 2sqrt2xy + 4sqrt2yz - 8xz`
Verify that `x^3+y^3+z^3-3xyz=1/2(x+y+z)[(x-y)^2+(y-z)^2+(z-x)^2]`
Without actually calculating the cubes, find the value of the following:
(–12)3 + (7)3 + (5)3
Evaluate the following using identities:
(399)2
Simplify the following products:
`(1/2a - 3b)(1/2a + 3b)(1/4a^2 + 9b^2)`
Write in the expanded form:
`(m + 2n - 5p)^2`
If 2x+3y = 13 and xy = 6, find the value of 8x3 + 27y3
Find the following product:
If \[x^2 + \frac{1}{x^2} = 102\], then \[x - \frac{1}{x}\] =
75 × 75 + 2 × 75 × 25 + 25 × 25 is equal to
Use the direct method to evaluate :
(4+5x) (4−5x)
Evaluate: (9 − y) (7 + y)
Expand the following:
(m + 8) (m - 7)
If p + q = 8 and p - q = 4, find:
pq
If p + q = 8 and p - q = 4, find:
p2 + q2
If 2x + 3y = 10 and xy = 5; find the value of 4x2 + 9y2
Simplify:
(7a +5b)2 - (7a - 5b)2
Simplify:
(1 + x)(1 - x)(1 - x + x2)(1 + x + x2)
Find the following product:
`(x/2 + 2y)(x^2/4 - xy + 4y^2)`
Find the value of x3 + y3 – 12xy + 64, when x + y = – 4
