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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

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)

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

7

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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.

Suggest Corrections

Similar questions

Q. The number of solutions of the equation

\frac{x}{7} = {x}

is
(where {.} is the fractional part function)

Q. The number of solutions of the equation

\frac{x}{7} = {x}

is
(where {.} is the fractional part function)

Q. The number of solutions of the equation

[x] + 2 {- x} = 3 x

, is

(where [ ] represents the greatest integer function and {x} denotes the fractional part of x)

Q. The number of solution(s) of the equation

[x] + 2 {- x} = 3 x

, is

/

are (where

[]

represents the greatest integer function and

{x}

denotes the fractional part of x

)

Q. The number of real solution(s) of the equation

2 [x] = x + {x}

is
(

[.]

denotes the greatest integer function and

{.}

denotes the fractional part function)

Join BYJU'S Learning Program

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)