Fsc Part 1 Mathematics (Complete Solution)

Q7
Solve the Following equations (x - 1)(x + 5)(x + 8)(x + 2) - 880 = 0

(x - 1)(x + 5)(x + 8)(x + 2) - 880 = 0

Solutions

As
-1 + 5 + 8 + 2
2
=
14
2
= 7, So we can write

[(x - 1)(x + 8)] [(x + 5)(x + 2)] - 880 = 0
(x2 + 8x - 1x - 8)(x2 + 2x + 5x + 10) - 880 = 0
(x2 + 7x - 8)(x2 + 7x + 10) - 880 = 0

Let x2 + 7x = t and Put in the equation

(t - 8)(t + 10) - 880 = 0
(t2 + 10t -8t -80) - 880 = 0
t2 + 2t -80 - 880 = 0
t2 + 2t - 960 = 0

By Quadratic Formula, we have

t =
-(2) ±
(2)2 - 4(1)(-960)
2(1)
t =
-2 ±
4 + 3840
2
t =
-2 ±
3844
2
t =
-2 ±
(62)2
2
t =
-2 ± 62
2

Either      
t =
-2 - 62
2
     OR      
t =
-2 + 62
2
t =
-64
2
t =
60
2
t = -32 t = 30

By Letting t = x2 + 7x,       Putting the value of t, we get
x2 + 7x = -32      OR       x2 + 7x = 30
x2 + 7x + 32 = 0 -----------------(i) x2 + 7x - 30 = 0 -----------------(ii)

By Equation (i)       x2 + 7x + 32 = 0

Using the Quadratic formula, we have

x =
-(7) ±
(7)2 - 4(1)(32)
2(1)
x =
-7 ±
49 - 128
2
x =
-7 ±
-79
2

By Equation (ii)       x2 + 7x - 30 = 0

Using the Quadratic formula, we have

x =
-(7) ±
(7)2 - 4(1)(-30)
2(1)
x =
-7 ±
49 + 120
2
x =
-7 ±
169
2
x =
-7 ±
(13)2
2
x =
-7 ± 13
2
Either        
x =
-7 - 13
2
        OR        
x =
-7 + 13
2
x =
-20
2
x =
6
2
x = -10
x = 3


Hence the Solution Set of given equation is
{ -10, 3 ,   
-7 -
-79
2
,   
-7 +
-79
2
}

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