Fsc Part 1 Mathematics (Complete Solution)

Q1
Solve the Following equations

x4 - 6x2 + 8 = 0
Solution

Putting x2 = t 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
Putting the values of a, b, and c in the formula

t =
-(-6) ±
(-6)2 - 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

Putting t = x2, we get
x2 = 2
x2 = 4
x = ±
2
x = ±
4
x = ±
2
x = ± 2

Hence Solution set = { -2, - 2, 2, 2 }

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