CAT 2020 Exam Shift 1 Solved Paper

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Question : 75 of 76

Marks: +1, -0

The number of distinct real roots of the equation

(x+\;{1}/{x})^{2}-3(x+\;{1}/{x})+2=0

equals

Your Answer:

Solution:

Let

x+\;{1}/{x}=a

The given equation becomes,

a^{2}-3 a+2=0 \;\; a=2

or 1 i.e

x+\;{1}/{x}=2

or

x+\;{1}/{x}=1

since

x

is real,

x+\;{1}/{x} ≠ 1 ; ∴ x+\;{1}/{x}=2

∴

The number of solutions

=1

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