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 √(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.