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Question

Solve for x:x > 1x


A

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B

U

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C

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D

[1,)

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Solution

The correct option is C


We may think of simple squaring & getting the values of x like shown below

x > 1x

Squaring,

x2 > 1 - x

x2 - x - 1 > 0 x ∈ (,152) U (1+52,)------(1)

But sometimes, squaring gives extra solution which don't satisfy the original inequality.

For eg, at x = 2 2 > 12

2 > 1 (not valid)

So, first we carefully see possible values of x from original inequality x > 1x

Square root always gives 1x ≥ 0

So, x > 1x x is always positive ------------(2)

Also in 1x, 1-x ≥ 0

1 ≥ x

x ≤ 1--------------(3)

Intersection of (1), (2) and (3) gives

x ∈ (512,1]


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