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Question

Solve for x:2(x2+1x2)9(x+1x)+14=0

A
12,1,2
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B
12,1,2
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C
12,1,4
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D
12,1,4
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Solution

The correct option is A 12,1,2
Let x+1x=t
x2+1x2+2=t2
x2+1x2=t22
Substituting these in the equation, we get
2(t22)9t+14=0
2t29t+10=0
(t2)(2t5)=0
t=2 or t=52

Case 1) t=2
x+1x=2
(x1)2=0
x=1

Case 2) t=52
x+1x=52
2x25x+2=0
(x2)(2x1)=0
x=2 or x=12

x={12,1,2}

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