CameraIcon

SearchIcon

MyQuestionIcon

1

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

Greatest Integer Function

If [x] is the...

Question

If [x] is the integral part of a real number x. Then, solve $[2 x] - [x + 1] = 2 x$ .

Open in App

Solution

$[2 x] - [x + 1] = 2 x => [2 x] - [x] - 1 = 2 x => [x] = 2 x + 1$
Here since $[x]$ is an integer,
Therefore $2 x + 1$ is also an integer.
And hence
$x = 2 x + 1$
$=> x = - 1$

Suggest Corrections

thumbs-up

0

Similar questions

x

be a real number

[x]

denotes the greatest integer function, and

{x}

denotes the fractional part and

(x)

denotes the least integer function,then solve the following.

[2 x] - 2 x = [x + 1]

Q. Solve the following equations:
(i)

\sqrt{2 x - 4} - \sqrt{x + 5} = 1

\sqrt{x} + \sqrt{x - \sqrt{1 - x}} = 1

x^{2} - 4 x + [x] + 3 = 0

[x]

denotes the integral part of

x

Q. We call a a good number if inequality

\frac{{2 x}^{2} + 2 x + 3}{x^{2} + x + 1} \leq a

is satisfied for any real x. Find the smallest good integral number

Q. let {x} and [x] denote the fractional and integral part of real number x respectively. Solve 4 {x} = x + [x] . Three times the non integral solution is

- (x - 3) + 4 > - 2 x + 5

x

is a real number.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Some Functions and Their Graphs

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Greatest Integer Function

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon