First slide

Theory of equations

Question

If [y] denote the greatest integer $< y,$ and $2 {[\frac{x}{8}]}^{2} + 3 [\frac{x}{8}] = 20$ then $x$ lies in the smallest interval $[a, b)$ where $b - a$ is equal to

Moderate

A

6
B

5
C

4
D

8

Solution

$2 {[\frac{x}{8}]}^{2} + 3 [\frac{x}{8}] - 20 = 0$
$\Rightarrow [\frac{x}{8}] = \frac{5}{2} or - 4$
As $[\frac{x}{8}]$ is an integer, we take
$[\frac{x}{8}] = - 4 \Rightarrow - 4 \leq x / 8 < - 3$
$\Rightarrow - 32 \leq x < - 24$ Thus, $a = - 32,$ and $b = - 24$ . Therefore, $b - a = 8$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App