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04 Jul 2019, 06:21
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What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?
A. -20
B. -5
C. -4
D. 0
E. 20
A. -20
B. -5
C. -4
D. 0
E. 20
04 Jul 2019, 06:21
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Official Solution:
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?
A. -20
B. -5
C. -4
D. 0
E. 20
Denote \(|x+2|\) as \(a\)
We get \(a^2 - 5a = -6\)
Solving quadratics gives \(a =3\) or \(a=2\)
Thus, \(|x+2|=3\) or \(|x+2|=2\)
Further solving gives, \(x=1\), \(x=-5\), \(x=0\), or \(x=-4\).
The product of those values is 0.
Answer: D
What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?
A. -20
B. -5
C. -4
D. 0
E. 20
Denote \(|x+2|\) as \(a\)
We get \(a^2 - 5a = -6\)
Solving quadratics gives \(a =3\) or \(a=2\)
Thus, \(|x+2|=3\) or \(|x+2|=2\)
Further solving gives, \(x=1\), \(x=-5\), \(x=0\), or \(x=-4\).
The product of those values is 0.
Answer: D
21 Nov 2019, 08:20
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What is the product of all possible solutions of the equation \(|x + 2|^2 - 5|x + 2| = -6\)?
A. -20
B. -5
C. -4
D. 0 --> correct: Quick solution:check the answer choices, it has 0--> so can 0 satisfies the equation? --> yes --> so the answer is D
E. 20
Details solution:
\(|x + 2|^2 - 5|x + 2| = -6\)?
assume, |x + 2| = y
so y^2-5y+6=0
=> (y-3)(y-2)=0
=> y = 3 or 2
=> |x + 2| = 3 or 2
=> x+2 = +3 or -3 or +2 or -2
=> x = 1 or -5 or 0 or -4
So the product of all possible solutions of the equation = (1)*(-5)*(0)*(-4)=0 --> so the answer is D
A. -20
B. -5
C. -4
D. 0 --> correct: Quick solution:check the answer choices, it has 0--> so can 0 satisfies the equation? --> yes --> so the answer is D
E. 20
Details solution:
\(|x + 2|^2 - 5|x + 2| = -6\)?
assume, |x + 2| = y
so y^2-5y+6=0
=> (y-3)(y-2)=0
=> y = 3 or 2
=> |x + 2| = 3 or 2
=> x+2 = +3 or -3 or +2 or -2
=> x = 1 or -5 or 0 or -4
So the product of all possible solutions of the equation = (1)*(-5)*(0)*(-4)=0 --> so the answer is D
