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M15#37

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M15#37 [#permalink] New post 25 May 2012, 08:28
there is a question in test m15

a^2-b^2=b^2-c^2.Is a=|b|

1)b=|c|
2)b=|a|

from 1 we get a^2=b^2

a=root b^2

or a=|b|

but in answer its given

a^2=b^2
so |a|=|b|


i have doubt regarding mod

|a|=root a^2

so above how can we write a^2=|a|
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Re: M15#37 [#permalink] New post 25 May 2012, 11:45
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mrinal2100 wrote:
there is a question in test m15

a^2-b^2=b^2-c^2.Is a=|b|

1)b=|c|
2)b=|a|

from 1 we get a^2=b^2

a=root b^2

or a=|b|

but in answer its given

a^2=b^2
so |a|=|b|


i have doubt regarding mod

|a|=root a^2

so above how can we write a^2=|a|


I guess your main question is about the following issue is why is \sqrt{x^2}=|x| true.

The point here is that as square root function can not give negative result then \sqrt{some \ expression}\geq{0}.

So \sqrt{x^2}\geq{0}. But what does \sqrt{x^2} equal to?

Let's consider following examples:
If x=5 --> \sqrt{x^2}=\sqrt{25}=5=x=positive;
If x=-5 --> \sqrt{x^2}=\sqrt{25}=5=-x=positive.

So we got that:
\sqrt{x^2}=x, if x\geq{0};
\sqrt{x^2}=-x, if x<0.

What function does exactly the same thing? The absolute value function: |x|=x, if x\geq{0} and |x|=-x, if x<0. That is why \sqrt{x^2}=|x|.

Hope it helps.
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Re: M15#37 [#permalink] New post 27 May 2012, 01:17
mrinal2100 wrote:
there is a question in test m15

a^2-b^2=b^2-c^2.Is a=|b|

1)b=|c|
2)b=|a|

from 1 we get a^2=b^2

a=root b^2

or a=|b|

but in answer its given

a^2=b^2
so |a|=|b|


i have doubt regarding mod

|a|=root a^2

so above how can we write a^2=|a|



here,
a^2=b^2
==> |a|=|b|
because here a &b both are variable.

|a|=root a^2; in all cases, but when you are equating a variable to variable a^2=b^2,
==> |a|=|b|, you have to right it this way.
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Re: M15#37   [#permalink] 27 May 2012, 01:17
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