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 a3 – 3a2b + 3ab2 – b3 + 8
Evaluate:
(i) (a + b)(a - b)
(ii) (a2 + b2)(a + b)(a - b); using the result of (i).
(iii) (a4 + b4)(a2 + b2)(a + b)(a - b); using the result of (ii).
Multiply: (2x - 3y)(2x + 3y)
Divide: 4a2 + 4a + 1 by 2a + 1
Divide: 8a2 + 4a - 60 by 2a - 5
The variable in the expression 16x – 7 is __________
Write the variables, constant and terms of the following expression
7p – 4q + 5
Write the variables, constant and terms of the following expression
29x + 13y
–b – 0 is equal to ______.
The value of 3x2 – 5x + 3 when x = 1 is ______.
