Fsc Part 1 Mathematics (Complete Solution)

Q6
Find values of x if

(i)    
 
3 1 x
-1 3 4
x 1 0
 
  = -30

SOLUTION:

   
 
3 1 x
-1 3 4
x 1 0
 
  = -30
  3
 
3 4
1 0
 
  - 1 
 
-1 4
x 0
 
  +  x
 
-1 3
x 1
 
=-30

3(0-4)-1(0-4x)+x(-1-3x)=-30

-12+4x-x-3x+30=0

-3x2+3x+18=0

x2-x-6=0

x2-3x+2x-6=0

x(x-3)+2(x-3)=0

(x+3)(x+2)=0

x-3=0                     ,      x+2=0

x=3                        ,    x=-2



(ii)    
 
x-1 3
-1 x+1 2
2 -2 x
 
  = 0

SOLUTION:

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

x2 +x+4-(x-1)(-x-4)+3(2-2x-2)=0

x2 +x+4+(x-1)(x+4)-6x=0

x2+x+4+x2-x+4x-4-6x=0

2x2-2x=0

2x(x-1)=0

2x=0              , x-1=0

x=0                ,x=1



(iii)    
 
2 1
2 x 2
3 6 x
 
  = 0

SOLUTION:

   
 
2 1
2 x 2
3 6 x
 
  = 0
  1
 
x 2
6 x
 
  - 2 
 
2 2
3 x
 
  + 1
 
2 x
3 6
 
=0

x2-12-2(2x-6)+12-3x=0

x2-12-4x+12+12-3x=0

x2-7x+12=0

(x-4)(x-3)=0

x-4=0     , x-3=0

x=4       , x=3

 

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