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Question

If α,β are the roots of the equation x23x+1=0, then the equation with roots 1α2,1β2 will be

A
x2x1=0
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B
x2+x1=0
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C
x2+x+2=0
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D
none of these
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Solution

The correct option is A x2x1=0
α,β are the roots of the equation x23x+1=0
α23α+1=0 ------(1)
Let 1α2=y
α=2+1y
From (1), we get
(2+1y)23(2+1y)+1=0
(2y+1)2y23(2y+1)y+1=0
y2y1=0
The equation with roots 1α2,1β2 is x2x1=0
Hence, option A.

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