Question

Total number of non-negative integral solutions of 2x + y + z = 21 is

Joshi sir comment

 

You can solve this question by the following method

possile algebric expression for the given equation is

(x0+x2+x4+........+x20)(x0+x1+x2+..................+x21)(x0+x1+x2+x3+....................x21)                 (i)

Here three brackets are for x , y and z, and powers are based on the range of least to greatest possile values of x, y, z

on solving eq (i) will become (x0+x2+x4+...........+x20)(1-x22)2(1-x)-2

now we have to calculate coefficient of x21 in this expression so (1-x22)2 can be omitted

general term of (1-x)-2 is (r+1)xr

so required coefficient = 22+20+18+16+14+12+10+8+6+4+2 = 132

Solution by Joshi sir.

 

You can solve this question by the following method

possile algebric expression for the given equation is

(x0+x2+x4+........+x20)(x0+x1+x2+..................+x21)(x0+x1+x2+x3+....................x21)                 (i)

Here three brackets are for x , y and z, and powers are based on the range of least to greatest possile values of x, y, z

on solving eq (i) will become (x0+x2+x4+...........+x20)(1-x22)2(1-x)-2

now we have to calculate coefficient of x21 in this expression so (1-x22)2 can be omitted

general term of (1-x)-2 is (r+1)xr

so required coefficient = 22+20+18+16+14+12+10+8+6+4+2 = 132

 

Read 1 Solution.

write it as , x+x+y+z=21

here 0 can be included so number of values are 24C3/2 .

NIKHIL VARSHNEY 12 year ago is this solution helpfull: 11 35

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