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

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Re: If |a+b|=|a-b|, then a*b must be equal to: [#permalink]

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New post 05 Jan 2015, 05:49
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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New post 05 Jan 2015, 06:07
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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New post 05 Jan 2015, 06:39
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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Re: If |a+b|=|a-b|, then a*b must be equal to:   [#permalink] 03 Mar 2017, 10:47

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