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Q1. How many roots does this equation possess? 3 |x| -|2-|x||=1

Q1. How many roots does this equation possess?


3|x|-|2-|x||=1

Grade:

1 Answers

Pratham Ashish
17 Points
12 years ago

hi , rewrite the eq. as

    3|x|-1 = |2-|x||

 or, we can write

      3|x|-1 =  ||x|-2|

we will now do the graphical analysis of both the function  3|x|-1   &  ||x|-2| .

if the graphs will intersect at apoint then at this point both the function will be equal

& this point will be the solu. of our eq.

 

 

4309-121_4788_3.bmp

we can  clearly say that there are only two solu. of the given eq.

 to draw the graph of first one,

1 . first we draw the 3^x . changing its -x axis by +xaxis we will get 3|x| . by pulling it downward  at a unit distance we will make graph of 3|x| -1

for second function,

  2.  draw the |x|  & pull it by 2 unit down ward . then we will invert that part of graph which is below x - axis  . this will be the graph of    ||x|-2|.

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