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

Given:

The set is

To find:

Whether the given set is empty or not.

Solution:

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

We have,

We need to find the solutions of and . The common solutions of these two equations are the elements of given set.

          ...(i)

And,

        ...(ii)

From (i) and (ii) it is clear that, there is no common value of x which satisfy both equations   and .

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

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step-by-step explanation: