Advertisements
Advertisements
Question
Find the value of 27x3 + 8y3, if 3x + 2y = 20 and xy = \[\frac{14}{9}\]
Advertisements
Solution
Given `3x+2y = 20,xy = 14/9`
On cubing both sides we get,
`(3x+ 2y)^3 = (20)^3`
We shall use identity `(a+b)^3 = a^3 + b^3 + 3ab(a+b)`
`27x^3 + 8y^3 + 3(3x)(2y)(3x+2y) = 20 xx 20 xx 20`
`27x^3 + 8y^3 + 18 (xy)(3x+ 2y)= 8000`
`27x^3 + 8y^3 + 18 (14/9)(20) = 8000`
` 27x^3 + 8y^3 = 8000 - 560`
`27x^3 + 8y^3 = 7440`
Hence the value of ` 27x^3 + 8y^3 `is 7440 .
APPEARS IN
RELATED QUESTIONS
Use suitable identity to find the following product:
(x + 4) (x + 10)
Use suitable identity to find the following product:
(3x + 4) (3x – 5)
Use suitable identity to find the following product:
`(y^2+3/2)(y^2-3/2)`
Simplify the following products:
`(x/2 - 2/5)(2/5 - x/2) - x^2 + 2x`
Simplify: `(a + b + c)^2 - (a - b + c)^2`
Evaluate the following:
(98)3
If \[x + \frac{1}{x} = 3\], calculate \[x^2 + \frac{1}{x^2}, x^3 + \frac{1}{x^3}\] and \[x^4 + \frac{1}{x^4}\]
Simplify of the following:
(x+3)3 + (x−3)3
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]
If x = −2 and y = 1, by using an identity find the value of the following
Use identities to evaluate : (502)2
Use the direct method to evaluate the following products :
(3x – 2y) (2x + y)
Use the direct method to evaluate :
`(3/5"a"+1/2)(3/5"a"-1/2)`
Simplify by using formula :
`("a" + 2/"a" - 1) ("a" - 2/"a" - 1)`
Evaluate, using (a + b)(a - b)= a2 - b2.
15.9 x 16.1
If x + y = 9, xy = 20
find: x2 - y2.
If `x + (1)/x = 3`; find `x^2 + (1)/x^2`
If `"r" - (1)/"r" = 4`; find : `"r"^4 + (1)/"r"^4`
Factorise the following:
9x2 + 4y2 + 16z2 + 12xy – 16yz – 24xz
