QJEEM20Mabb19: JEE Main 2020 Mathematics - Class 11 JEEM20Mabb19 Solution: Let [t] denote the greatest integer ≤ t. Then the equation in…

Question

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Let [t] denote the greatest integer

\leq

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} + 3 y - y - 3 = 0

\Rightarrow

(y - 1) (y + 3) = 0

[x] = 1 o r [x] = - 3

∴

x \in [1, 2) & \in [- 3, - 2)

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