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Question

Solve the reciprocal equation x43x3+4x23x+1=0

A
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B
1
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C
3
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D
1
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Solution

The correct option is B 1
We see that it is a reciprocal equation, so we divide it by x2:

x23x+43x+1x2=0

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

We will now substitute x+1x=u

By squaring it, and solve further we get

x2+1x2=u22

We plug back into the equation to get

u23u+2=0

The solutions are u1=1,u2=2
So either x+1x=1 or 2

From the first solution we get
x2x+1=0 which has no solution
From the second one we get
x22x+1=0
x=1

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