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The solution set of |x +1/x| + |x +1| = (x+1)^2 /|x|

The solution set of  |x +1/x| + |x +1| = (x+1)^2 /|x|

Grade:11

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
6 years ago
Hello Student,
\\|x+{1 \over x}|+|1+x|={(x+1)^2 \over x} \\=>|x+{1 \over x}|+|1+x|=x+{2}+{1 \over x} \\$we will consider 3 partition$ \\x \in(-\infty,-1],(-1,0),(0,\infty) \\$for the first$ \\-x-{1 \over x}-1-x=x+{2}+{1 \over x} \\=>3x^2+3x+2=0 \\D<0$ so no roots$ \\$considering second interval$ \\=>-x-{1 \over x}+1+x=x+{2}+{1 \over x} \\=>x^2+x+2=0 \\$again $D<0 \\$considering third interval$ \\=>x+{1 \over x}+1+x=x+{2}+{1 \over x} \\=>1+x=2 \\=>x=1

Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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