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If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the
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09 Feb 2020, 15:51
09 Feb 2020, 15:51
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If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following must be true?
A. ab < 0
B. ab > 0
C. a - b > 0
D. a + b < 0
E. a + b > 0
Kudos for the right answer and explanation
A. ab < 0
B. ab > 0
C. a - b > 0
D. a + b < 0
E. a + b > 0
Kudos for the right answer and explanation
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Re: If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the
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10 Feb 2020, 00:53
10 Feb 2020, 00:53
2
Carcass wrote:
If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the following must be true?
A. ab < 0
B. ab > 0
C. a - b > 0
D. a + b < 0
E. a + b > 0
Kudos for the right answer and explanation
A. ab < 0
B. ab > 0
C. a - b > 0
D. a + b < 0
E. a + b > 0
Kudos for the right answer and explanation
The concept to be used: For all \(a\) and \(b\), we have: \(|a| + |b| ≥ |a + b|\)
For example:
#1. \(a = 2, b = 3 : |a| + |b| = |2| + |3| = 2 + 3 = 5\) and \(|a + b| = |2 + 3| = 5\) => \(|a| + |b| = |a + b|\)
#2. \(a = -2, b = -3 : |a| + |b| = |-2| + |-3| = 2 + 3 = 5\) and \(|a + b| = |-2 - 3| = 5\) => \(|a| + |b| = |a + b|\)
#3. \(a = -2, b = 3 : |a| + |b| = |-2| + |3| = 2 + 3 = 5\) and \(|a + b| = |-2 + 3| = 1\) => \(|a| + |b| > |a + b|\)
Note:
# \(|a| + |b| = |a + b|\) if \(a\) and \(b\) are of the same sign
# \(|a| + |b| > |a + b|\) if \(a\) and \(b\) are of opposite signs
We have been given that: \(|a| + |b| = |a + b|\) => \(a\) and \(b\) are of the same sign
Thus, \(a*b > 0\)
Answer B
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If |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0, then which of the
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23 Dec 2021, 09:58
23 Dec 2021, 09:58
1
Given that |a| + |b| = |a + b|, a ≠ 0, and b ≠ 0 and we need to tell which option choice must be true
Now, |a| + |b| = |a +b|
That means Sum of Modulus of two numbers is equal to modulus of their sum, now this is true only when the two numbers have the same sign
i.e. Either both are positive or both are negative
(Check out this video to know more about Absolute values/Modulus of a number)
=> a and b have the same sign
Now, if both have the same sign then their product will always be > 0
Because POSITIVE * POSITIVE = POSITIVE and NEGATIVE * NEGATIVE = POSITIVE
(Check out this video to know more about basics of Inequalities)
=> ab > 0
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
Now, |a| + |b| = |a +b|
That means Sum of Modulus of two numbers is equal to modulus of their sum, now this is true only when the two numbers have the same sign
i.e. Either both are positive or both are negative
(Check out this video to know more about Absolute values/Modulus of a number)
=> a and b have the same sign
Now, if both have the same sign then their product will always be > 0
Because POSITIVE * POSITIVE = POSITIVE and NEGATIVE * NEGATIVE = POSITIVE
(Check out this video to know more about basics of Inequalities)
=> ab > 0
So, Answer will be B
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
