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If 3x+2 - 9-1/ x> 0 , then the interval of x can be
- a)x ∈ (0,∞)
- b)x ∈ (-5, 5)
- c)x ∈ R
- d)x ∈ (-∞, 0)
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If 3x+2 - 9-1/ x 0 , then the interval of x can bea)x (0,)b)x (-5, 5...
Most Upvoted Answer
If 3x+2 - 9-1/ x 0 , then the interval of x can bea)x (0,)b)x (-5, 5...
Explanation:
Given Equation:
3x + 2 - 9 - 1/x > 0
Simplify the Equation:
3x - 7 - 1/x > 0
3x - 1/x > 7
Find the Critical Points:
To find the critical points, set the expression equal to 0:
3x - 1/x = 7
3x^2 - 7x - 1 = 0
Using the quadratic formula, we find the roots of the equation:
x = (7 ± √(49 + 12))/6
x = (7 ± √61)/6
Interval Analysis:
Since the inequality is greater than 0, we need to find where the expression is positive.
This occurs when x is greater than the larger root or less than the smaller root:
x > (7 + √61)/6 or x < (7="" -="" />
Final Interval:
Therefore, the interval of x where the given inequality holds true is:
x > (7 + √61)/6, which can be written as x > (7 + √61)/6
Therefore, the correct option is (A) x > (7 + √61)/6.
Given Equation:
3x + 2 - 9 - 1/x > 0
Simplify the Equation:
3x - 7 - 1/x > 0
3x - 1/x > 7
Find the Critical Points:
To find the critical points, set the expression equal to 0:
3x - 1/x = 7
3x^2 - 7x - 1 = 0
Using the quadratic formula, we find the roots of the equation:
x = (7 ± √(49 + 12))/6
x = (7 ± √61)/6
Interval Analysis:
Since the inequality is greater than 0, we need to find where the expression is positive.
This occurs when x is greater than the larger root or less than the smaller root:
x > (7 + √61)/6 or x < (7="" -="" />
Final Interval:
Therefore, the interval of x where the given inequality holds true is:
x > (7 + √61)/6, which can be written as x > (7 + √61)/6
Therefore, the correct option is (A) x > (7 + √61)/6.
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If 3x+2 - 9-1/ x 0 , then the interval of x can bea)x (0,)b)x (-5, 5)c)x Rd)x (-, 0)Correct answer is option 'A'. Can you explain this answer?
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If 3x+2 - 9-1/ x 0 , then the interval of x can bea)x (0,)b)x (-5, 5)c)x Rd)x (-, 0)Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If 3x+2 - 9-1/ x 0 , then the interval of x can bea)x (0,)b)x (-5, 5)c)x Rd)x (-, 0)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 3x+2 - 9-1/ x 0 , then the interval of x can bea)x (0,)b)x (-5, 5)c)x Rd)x (-, 0)Correct answer is option 'A'. Can you explain this answer?.
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