Let S={x∈R :x≥0 & 2∣∣x√−3∣∣+x√ (x√−6)+6=0} . Then S:Contains exactly four elementsIs an empty setContains exactly one elementContains exactly two elements
Question
Let S={x∈R :x≥0 & 2∣∣x√−3∣∣+x√ (x√−6)+6=0} . Then S:Contains exactly four elementsIs an empty setContains exactly one elementContains exactly two elements
Solution
The given equation is a quadratic equation in terms of √x. Let's solve it step by step:
-
Let y = √x. Then the equation becomes: 2|y√-3| + y√(y√-6) + 6 = 0.
-
This equation is not defined for real numbers because of the terms √-3 and √-6, which are imaginary numbers.
-
Therefore, there are no real solutions to this equation.
-
Since the set S is defined as S={x∈R :x≥0}, and there are no real solutions to the equation, S is an empty set.
So, the correct answer is: S is an empty set.
Similar Questions
Let S := {x ∈ R : x > 0}. Find inf S
8. Let (X, d) be a metric space and let S ⊆ X. Prove that dS (x) = 0 if and only if x ∈ S
Let S={x∈R :x≥0 & 2∣∣x√−3∣∣+x√ (x√−6)+6=0} . Then S:Contains exactly four elementsIs an empty setContains exactly one elementContains exactly two elements
Write a logical statement that says ”b is not an upper bound of S”using quantifier(s), ≥, and using the negation symbol
Write a logical statement that says ”b is not an upper bound of S”using quantifier(s) and ≥, but do not use the negation symbol
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.