Solve the inequality -
0.5 / x - x² - 1 < 0
Answers
0.5 / x - x² - 1 < 0
0.5 / - 1 ( x² - x + 1 ) < 0
Hence ,
x ∈ ( - ∞ , + ∞ )
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Concept:
"A connection is called an inequality if two real numbers or algebraic expressions are connected by the symbols ">," "," "," or "."
For instance, x>3 (x should be greater than 3)
If there is just one variable, the inequality is said to have an open sentence.
Instance: x 6 (x is less than 6)
Double Inequalities: If the statement demonstrates a double relation between the expressions or the numbers, the inequality is said to be a double inequality.
Instance: 3 x 8 ( x is greater than or equal to 3 and less than 8)
Expressions with linear inequalities compare any two values using inequality symbols like "," ">," "," or "." These values could be either numerical, algebraic, or both. Examples of numerical inequality include 1011 and 20>17, whereas algebraic inequalities include x>y, y>19-x, and x z > 11 (also called literal inequalities)
Given:
0.5 / x - x² - 1 < 0
Find:
Find the range of x
Solution:
0.5 / x - x² - 1 < 0
∵x - x² - 1 is always negative and 0.5 is a constant no.
So we can write,
x∈(-∞,∞) or x∈R
Therefore, x∈(-∞,∞) or x∈R
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