Check whether A{x:x2 =25 and 6x= 125} is an empty set or not

Question

asked Jul 16, 2022 124k views

1 Answer

Markus Kauppinen · Answer 1 · 2022-07-20T12:44:45+0000

Given:

The set is

$A=\{x:x^2=25\text{ and }6x=125\}$

To find:

Whether the given set is empty or not.

Solution:

A set is called empty set if it has no elements.

We have,

$A=\{x:x^2=25\text{ and }6x=125\}$

We need to find the solutions of
x^2=25 and
6x=125 . The common solutions of these two equations are the elements of given set.

x^2=25

$x=\pm √(25)$

$x=\pm 5$

x=5,-5 ...(i)

And,

6x=125

x=(125)/(6)

$x\approx 20.83$ ...(ii)

From (i) and (ii) it is clear that, there is no common value of x which satisfy both equations
x^2=25 and
6x=125 .

Since there is no element in set A, therefore, the given get A is an empty set.