The number of solutions of the equation x 7 - x is where - is the fractional part function

X 7 = {x} We know that, 0≤{x} lt;1 ⇒ 0≤ x 7 lt;1 ⇒ 0≤ nbsp;x lt;7 ...(1) When x ∈ [6, 7) x 7 = x 6 ⇒ x =7 which is not possible from eqn(1) Theref ...

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Standard XIII

Mathematics

Graph of Fractional Part Function

The number of...

Question

The number of solutions of the equation $\frac{x}{7} = {x}$ is
(where {.} is the fractional part function)

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Solution

The correct option is C $6$
$\frac{x}{7} = {x}$
We know that, $0 \leq {x} < 1$
$\Rightarrow 0 \leq \frac{x}{7} < 1$
$\Rightarrow 0 \leq x < 7 . . . (1)$

When $x \in [6, 7)$
$\frac{x}{7} = x - 6$
$\Rightarrow x = 7$
which is not possible from eqn $(1)$
Therefore, the given equation has $6$ solutions.

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The number of solutions of the equation x7={x} is (where {.} is the fractional part function)

The correct option is C 6x7={x} We know that, 0≤{x}<1 ⇒0≤x7<1 ⇒0≤x<7 ...(1) When x∈[6,7) x7=x−6 ⇒x=7 which is not possible from eqn(1) Therefore, the given equation has 6 solutions.

The number of solutions of the equation $\frac{x}{7} = {x}$ is
(where {.} is the fractional part function)