Fsc Part 1 Mathematics (Complete Solution)

Q8
Show that

 
x 1 1 1
1 x 1 1
1 1 x 1
1 1 1 x
 
  =(x+3)(x-1)3

SOLUTION:

L.H.S= 
 
x 1 1 1
1 x 1 1
1 1 x 1
1 1 1 x
 
  
     = 
 
x+3 x+3 x+3 x+3
1 x 1 1
1 1 x 1
1 1 1 x
 
  R1+(R2+R3+R4)
       = (x+3)
 
1 1 1 1
1 x 1 1
1 1 x 1
1 1 1 x
 
  
       = (x+3)
 
1 0 0
1 x-1 0 0
1 0 x-1 0
1 0 0 x-1
 
C2-C1
C3-C1
C4-C1  

Expand by R1

       = (x+3)
 
x-1 0 0
0 x-1 0
0 0 x-1
 
  
       = (x+3)(x-1)
 
x-1 0
0 x-1
 
  

=(x+3)(x-1)[(x-1)2-0]

=(x+3)(x-1)(x-1)2

=(x+3)(x-1)3

=R.H.S

Hence Proved

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