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Senior Manager  Status: Math is psycho-logical
Joined: 07 Apr 2014
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Re: If |a+b|=|a-b|, then a*b must be equal to:  [#permalink]

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I am not sure if the way I thought of the absolute value was correct, but here it is.

QUESTION: If |a+b|=|a-b|, then a*b must be equal to:

I thought that when there is an absolute value, we think of the "value" within it with no regards to the sign. So, I thought it could be:
a+b= a-b. If we move a to the other side, both a's get cancelled, which leads to b=-b. Moving -b to the other side it becomes 2b=0. So, b=0, which means that a*b must be equal to 0.
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Re: If |a+b|=|a-b|, then a*b must be equal to:  [#permalink]

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pacifist85 wrote:
I am not sure if the way I thought of the absolute value was correct, but here it is.

QUESTION: If |a+b|=|a-b|, then a*b must be equal to:

I thought that when there is an absolute value, we think of the "value" within it with no regards to the sign. So, I thought it could be:
a+b= a-b. If we move a to the other side, both a's get cancelled, which leads to b=-b. Moving -b to the other side it becomes 2b=0. So, b=0, which means that a*b must be equal to 0.

You are missing the second case there.

If a+b and a-b have the same sign, then we'd have a+b = a-b --> b=0 --> ab=0;
If a+b and a-b have the opposite signs, then we'd have a+b = -(a-b) --> a=0 --> ab=0.
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Re: If |a+b|=|a-b|, then a*b must be equal to:  [#permalink]

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Thank you for explaining. I have gone through the absolute values, but they keep creating some confusion.
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Re: If |a+b|=|a-b|, then a*b must be equal to:  [#permalink]

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Quote:
If |a+b|=|a-b|, then a*b must be equal to:

A. 1
B. -1
C. 0
D. 2
E. -2

niks18 Bunuel chetan2u pushpitkc

Let me know if below approach is correct:

|a+b| or |a-b| will always yield a positive value.
This is because a modulus always represents an ABSOLUTE distance
from number line.

So |a+b|=|a-b|
simplifies to
a + b = a - b
I can cancel a from both sides in all circumstances.
2b = 0 -> b = 0
or a*b = 0

Hope assumptions made by me are correct.
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If |a+b|=|a-b|, then a*b must be equal to:  [#permalink]

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Quote:
If |a+b|=|a-b|, then a*b must be equal to:

A. 1
B. -1
C. 0
D. 2
E. -2

niks18 Bunuel chetan2u pushpitkc

Let me know if below approach is correct:

|a+b| or |a-b| will always yield a positive value.
This is because a modulus always represents an ABSOLUTE distance
from number line.

So |a+b|=|a-b|
simplifies to
a + b = a - b
I can cancel a from both sides in all circumstances.
2b = 0 -> b = 0
or a*b = 0

Hope assumptions made by me are correct.

Ans here will be either A or B or both are 0..
And this is why..
You cannot remove modulus this way, you do know if B is greater or A or they are NEGATIVE..
So square both sides, since both are modulus..
a^2+b^2+2ab=a^2+b^2-2ab.....
4ab=0..
So either A or B or both are 0
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Re: If |a+b|=|a-b|, then a*b must be equal to:  [#permalink]

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chetan2u

Quote:
You cannot remove modulus this way, you do know if B is greater or A or they are NEGATIVE.

But we shall still always get END RESULT as positive on opening modulus.

|5| = 5

|- 5| = - (-5) = 5

Am I correct?
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Posts: 8308
Re: If |a+b|=|a-b|, then a*b must be equal to:  [#permalink]

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1
chetan2u

Quote:
You cannot remove modulus this way, you do know if B is greater or A or they are NEGATIVE.

But we shall still always get END RESULT as positive on opening modulus.

|5| = 5

|- 5| = - (-5) = 5

Am I correct?

Yes you are correct..
But |5-3|=|3-5| does not mean 5-3=3-5... That is 2=-2??
So square the MODULUS to get rid of Modulus
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Re: If |a+b|=|a-b|, then a*b must be equal to:  [#permalink]

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_________________ Re: If |a+b|=|a-b|, then a*b must be equal to:   [#permalink] 21 Apr 2019, 05:50

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