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12 Sep 2024, 01:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
45% (02:54) correct
55%
(02:34)
wrong
based on 130
sessions
History
Date
Time
Result
Not Attempted Yet
If |x| > |x|^2 − 5x + 6, what is the product of all integer values of x that satisfy the inequality?
A. 6
B. 12
C. 18
D. 24
E. 30
A. 6
B. 12
C. 18
D. 24
E. 30
12 Sep 2024, 11:00
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when |x| is positive,
\(x>x^2 − 5x + 6\)
\(=>x^2 − 6x + 6\)
Solving by the quadratic formula of \(x=\frac{-b±\sqrt{b^2-4ac}}{2a}\)
we get,
\(x= \frac{−(−6)±\sqrt{12}}{2*1}\)
=> x = \(3±\sqrt{3}\) ................... (i)
Again when |x| is negative,
\(-x>x^2 − 5x + 6\)
\(=>x^2 − 4x + 6\)
Solving by the quadratic formula, we get -
\(x= \frac{−(−4)±\sqrt{-8}}{2*1}\)
So, x got no solution here as the \(\sqrt{-8}\) has a negative value.
So From (i) we get,
\(3-\sqrt{3} < x < 3+\sqrt{3}\)
which is somewhere around, \(1.27 < x < 4.73\)
So all integers satisfying this are - 2, 3, 4
Product of them = \(2 * 3 * 4 = 24\)
OPTION D is the answer
\(x>x^2 − 5x + 6\)
\(=>x^2 − 6x + 6\)
Solving by the quadratic formula of \(x=\frac{-b±\sqrt{b^2-4ac}}{2a}\)
we get,
\(x= \frac{−(−6)±\sqrt{12}}{2*1}\)
=> x = \(3±\sqrt{3}\) ................... (i)
Again when |x| is negative,
\(-x>x^2 − 5x + 6\)
\(=>x^2 − 4x + 6\)
Solving by the quadratic formula, we get -
\(x= \frac{−(−4)±\sqrt{-8}}{2*1}\)
So, x got no solution here as the \(\sqrt{-8}\) has a negative value.
So From (i) we get,
\(3-\sqrt{3} < x < 3+\sqrt{3}\)
which is somewhere around, \(1.27 < x < 4.73\)
So all integers satisfying this are - 2, 3, 4
Product of them = \(2 * 3 * 4 = 24\)
OPTION D is the answer
General Discussion
