Question

check whether {x: x^2 = 25 and 6x = 15 } is an empty set or not ?​

Answer 1

Answer:

empty set

Step-by-step explanation:

${x}^{2} = 25 \\ x = 5 \\ \\ 6 \times x = 15 \\ 6 \times 5 \: \: is \: not \: equal \: \:to \: 15 \\ i.e \: 6 \times 5 = 15a \\ for \: some \: value \: a$

Answer 2

Answer :-

Empty set

Solution :-

Let, A = { x : x² = 25 and 6x = 15 }

Finding x when x² = 25

⇒ x² = 25

⇒ x = √25

⇒ x = ± 5

⇒ x = 5 or - 5

Finding x when 6x = 15

⇒ 6x = 15

⇒ x = 15 / 6

⇒ x = 2.5

Since, the value of x in both cases are different there is no value of x that satisfies the given rule.

So, the set A = Φ

Therefore the set { x : x² = 25 and 6x = 15 } is an empty set.