Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsNumber of Solutions (graph)Easy2 minQB

MathematicsEasyinteger

Number of real values of x , satisfying the equation $[x]^{2} - 5 [x] + 6 - sin x = 0 [$ . $] d e n o t in g$ the greatest integer function is

Answer:

Solution:

$[x] = \frac{5 \pm 25 + 4 s i n x - 24}{2.1}$

$= \frac{5 \pm 1 + 4 s i n x}{2}$

$- 1 \leq sin x \leq 1$

$- 4 \leq 4 sin x \leq 4$

$- 3 \leq 1 + 4 sin \leq 5$

$0 \leq 1 + 4 sin x \leq 5$

$\Rightarrow [x]$ is an integer $\Leftrightarrow sin x = 0$ $\Rightarrow [x] = 3$

$\Rightarrow x = π$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Number of Solutions (graph)

⏱ 2mℹ️ Source: QB

Loading discussions...