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Question

How many roots do. the following equations possess?
3 |x| |2 - |x|| = 1.

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Solution


3|x||2|x||=1 (given)
C1(0<x<2) C2(x>2) C3(2<x<0)
3x(2x)=1 3x(2x)=1 3x(2+x)=1
3x26x+1=0 3x26x1=0 3x2+6x+1=0
x=6±36126 x=6±436 x=6±266
x=6±266 x=6+436
So, 5 roots are there.

1227251_892665_ans_45d1f9c2b1b941b48ec20a60d3c6b5fe.jpg

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