Advertisements
Advertisements
प्रश्न
If 2x+3y = 13 and xy = 6, find the value of 8x3 + 27y3
Advertisements
उत्तर
In the given problem, we have to find the value of `8x^3 + 27y^3`
Given`2x + 3y = 13, xy = 6`
In order to find `8x^3 + 27y^3`we are using identity `(a+b )^3 = a^3 + b^3 + 3ab(a+b)`
`(2x + 3y )^3 = (13)^3`
`8x^3 + 27 y^3 + 3 (2x)(3y)(2x+ 3y)= 2197`
` 8x^3 + 27y^3 + 18xy (2x+ 3y) = 2197`
Here putting, `2x + 3y = 13, xy = 6`
`8x^3 + 27y^3 + 18 xx 6 xx 13 = 2197`
` 8x^3 + 27y^3 + 1404 = 2197`
` 8x^3 + 27y^3 = 2197 - 1404`
`8x^3+ 27y^3 = 793`
Hence the value of `8x^3 + 27y^3` is 793.
APPEARS IN
संबंधित प्रश्न
Write the following cube in expanded form:
(2x + 1)3
Factorise the following:
`27p^3-1/216-9/2p^2+1/4p`
If 9x2 + 25y2 = 181 and xy = −6, find the value of 3x + 5y
If 2x + 3y = 8 and xy = 2 find the value of `4x^2 + 9y^2`
Simplify `(x^2 + y^2 - z)^2 - (x^2 - y^2 + z^2)^2`
If a + b + c = 9 and ab + bc + ca = 23, find the value of a2 + b2 + c2.
Find the value of 64x3 − 125z3, if 4x − 5z = 16 and xz = 12.
Find the following product:
If x = 3 and y = − 1, find the values of the following using in identify:
\[\left( \frac{5}{x} + 5x \right)\] \[\left( \frac{25}{x^2} - 25 + 25 x^2 \right)\]
Evaluate:
253 − 753 + 503
Find the square of : 3a + 7b
If a - b = 7 and ab = 18; find a + b.
Use the direct method to evaluate :
(2+a) (2−a)
Evaluate: 20.8 × 19.2
Expand the following:
(2x - 5) (2x + 5) (2x- 3)
Simplify by using formula :
(x + y - 3) (x + y + 3)
Simplify by using formula :
(1 + a) (1 - a) (1 + a2)
Simplify:
`("a" - 1/"a")^2 + ("a" + 1/"a")^2`
Factorise the following:
4x2 + 20x + 25
Factorise the following:
25x2 + 16y2 + 4z2 – 40xy + 16yz – 20xz
