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Question

Let [t] denote the greatest integer t. Then the equation in x, [x]2+2[x+2]7=0 has

A
Exactly four integral solutions
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B
infinitely many solutions
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C
no integral solution
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D
exactly two solutions
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Solution

The correct option is B infinitely many solutions
Given: [x]2+2[x+2]7=0
[x]2+2[x]3=0
let [x]=y. Then,
y2+2y3=0
(y1)(y+3)=0
[x]=1 or [x]=3
x[1,2) or x[3,2)

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