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
Factorize `x^2 - 2sqrt2x - 30`
Divide: 25x2y by - 5y2
Divide: m2 − 2mn + n2 by m − n
Divide: 15x2 + 31xy + 14y2 by 5x + 7y
Divide: 6x3 + 5x2 − 21x + 10 by 3x − 2
Write in the form of an algebraic expression:
Perimeter (P) of a square is four times its side.
The constant term of the expression 2y – 6 is _________
Write the variables, constant and terms of the following expression
18 + x – y
If Rohit has 5xy toffees and Shantanu has 20yx toffees, then Shantanu has ______ more toffees.
Express the following properties with variables x, y and z.
Distributive property of multiplication over addition
