Let [t] denote the greatest integer [ ] t.

Question

Let [t] denote the greatest integer $$ \le $$ t. Then the equation in x,

[x]2 + 2[x+2] - 7 = 0 has :

Accepted Answer

$${[x]^2} + 2[x + 2] - 7 = 0$$

$$ \Rightarrow $$ $${[x]^2} + 2[x]  + 4 - 7 = 0$$

Using the property [x + n] = [x] + n ; n $$ \in $$ I

$$ \Rightarrow $$ $${[x]^2} + 2[x] - 3 = 0$$

let [x] = y

${y^2} + 3y - y - 3 = 0$

$$ \Rightarrow $$ $(y - 1)(y + 3) = 0$

$$[x] = 1\,or\,[x] =  - 3$$

$$ \therefore $$ $$x \in \left[ {1,2} \right)\,\& \, \in \left[ { - 3, - 2} \right)$$

Solutions · 1