Fsc Part 1 Mathematics (Complete Solution)

Q5
Solve the Following equations

x
2
5
   + 8 = 6x
1
5

Solution



Let x
1
5
    = t and Put in the given equation

t2 - 6t + 8 = 0
Comparing the given equation with at2 + bt + c = 0, we get
a = 1,
b = -6,
c = 8

By Quardratic formula, we have
t =
-b ±
b2 - 4ac
2a

t =
-(-6) ±
62 - 4(1)(8)
2(1)
t =
6 ±
36 - 32
2
t =
6 ±
4
2
t =
6 ± 2
2

Either        
t =
6 - 2
2
        OR        
t =
6 + 2
2
t =
4
2
t =
8
2
t = 2
t = 4



By letting x
1
5
    = t , Putting the value of t, we get



x
1
5
    
= 2
x
1
5
    
= 4
x = 25 x = 45
x = 32 x = 1024


Hence the Solution Set of given equation is {32, 1024}

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