Number of integral values of x , satisfying the equation [ x ] 2 - 5 [ x ] + 6 = 0 , where [ · ] denotes the greatest integer function is

Question

Number of integral values of $x$ , satisfying the equation ${[x]}^{2} - 5 [x] + 6 = 0,$ where $[\cdot]$ denotes the greatest integer function is _______.

Smart Achievers · Accepted Answer

(2)

$[x]$ $= \frac{5 \pm \sqrt{25 - 24}}{2 \cdot 1} = \frac{5 \pm \sqrt{1}}{2} = 3, 2$

Solution

Q.
Number of integral values of $x$ , satisfying the equation ${[x]}^{2} - 5 [x] + 6 = 0,$ where $[\cdot]$ denotes the greatest integer function is _______.

Ans.
(2)

$[x]$ $= \frac{5 \pm \sqrt{25 - 24}}{2 \cdot 1} = \frac{5 \pm \sqrt{1}}{2} = 3, 2$

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Solution

Q. Number of integral values of x, satisfying the equation [x]2-5[x]+6=0, where [·] denotes the greatest integer function is _______.

Ans. (2) [x]=5±25-242·1=5±12=3, 2

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Q.
Number of integral values of $x$ , satisfying the equation ${[x]}^{2} - 5 [x] + 6 = 0,$ where $[\cdot]$ denotes the greatest integer function is _______.

Ans.
(2)

$[x]$ $= \frac{5 \pm \sqrt{25 - 24}}{2 \cdot 1} = \frac{5 \pm \sqrt{1}}{2} = 3, 2$