Question

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

Answer 1

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.

$x^2=25$

$x=\pm \sqrt{25}$

$x=\pm 5$

$x=5,-5$           ...(i)

And,

$6x=125$

$x=\dfrac{125}{6}$

$x\approx 20.83$         ...(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.