Question

Find the number of integral solution of this equation x+y+z + w < 25 such that x> -2, y> 1. z>=0 and w >3.​

Answer 1

Answer:Solution

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Correct option is A)

Since x+y+z+t=29...(i)

and x,y,z,t are integers

∴x≥1,y≥2,z≥3,t≥0

⇒x−1≥0,y−2≥0,z−3≥0,t≥0

Let x  

1

​

=x−1,x  

2

​

=y−2,x  

3

​

=z−3

Or x=x  

1

​

+1,y=x  

2

​

+2,z=x  

3

​

+3 and then x  

1

​

≥0,x  

2

​

≥0,x  

3

​

≥0,t≥0

From (1),

x  

1

​

+1+x  

2

​

+1x  

3

​

+1+t=29

⇒ x  

1

​

+x  

2

​

+x  

3

​

+t=23

Hence total number of solutions

=  

23+4−1

C  

4−1

​

 

=  

26

C  

3

​

=  

1.2.3

26.25.24

​

=2600