M15#37

Question

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|

Bunuel · Answer

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.

321kumarsushant · Answer

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.

M15#37

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