Advertisements
Advertisements
प्रश्न
`(x/2 + y + z/3)^3 + (x/2 + (2y)/3 + z)^3 + (-(5x)/6 - y/3 - (4z)/3)^3`
Advertisements
उत्तर
Let `(x/2 + y + z/3) = a, (x/3 - (2y)/3 + z) = b, (-(5x)/6 - y/3 - (4z)/3) = c`
`a + b + c = x/2 + y + z/3 + x/3 - (2y)/3 + z - (5x)/6 - y/3 - (4z)/3`
`a + b + c = (x/2 + x/3 - (5x)/6) + (y - (2y)/3 - y/3) + (z/3 + z - (4z)/3)`
`a + b + c = (3x)/6 + (2x)/6 - (5x)/6 + (3y)/3 - (2y)/3 - y/3 + z/3 + (3z)/3 - (4z)/3`
`a + b + c = (5x - 5x)/6 + (3y - 3y)/3 + (4z - 4z)/3`
a + b + c = 0
∵ a + b + c = 0 `∴ a^3 + b^3 + c^3 = 3abc`
`∴ [x/2 + y + z/3]^3 + [x/3 - (2y)/3 + z]^3 + [-(5x)/6 - y/3 - (4z)/3]^3 = 3(x/2 + y + z/3)(x/3 - (2y)/3 + z)(-(5x)/6 - y/3 - (4z)/3)`
APPEARS IN
संबंधित प्रश्न
Get the algebraic expression in the following case using variables, constants and arithmetic operations.
Product of numbers y and z subtracted from 10.
If x − y = 7 and xy = 9, find the value of x2 + y2
Find the value of the following expression: 16x2 + 24x + 9, when \[x = \frac{7}{4}\]
The factors of x3 −x2y − xy2 + y3 are
Multiply: (2x + 3y)(2x - 3y)
Divide: m3 − 4m2 + m + 6 by m2 − m − 2
Solve the following equation.
3y + 4 = 5y − 6
The largest number of the three consecutive numbers is x + 1, then the smallest number is ________
The value of 7a – 4b when a = 3, b = 2 is
How many terms does a trinomial contain?
