InterviewSolution
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InterviewSolution
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For a `alt=0,`determine all real roots of theequation `x^2-2a|x-a|-3a^2=0.` |
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Answer» Correct Answer - `x={a(1-sqrt2),a (sqrt6-1)}` Here, `a ge 0` Given, `x^(2)-2a |x-a|-3a^(2)=0` Case I When `x ge a` `impliesx^(2)-2a(x-a)-3a^(2)=0` `impliesx^(2)-2ax -a^(2)=0` `impliesx=a +-sqrt2a` `" "[as a(1+sqrt2)ltaand a (1-sqrt2)gta]` `therefore"Neglecting" x=a(1+sqrt2)as x gea` `impliesx=a(1-sqrt2)" "...(i)` Case II When `x lt a impliesx^(2)+2a(x-a)-3a^(2)=0` `impliesx^(2)+2ax-5a^(2)=0impliesx=-aa+-sqrt6a` `" "[as a (sqrt6-1)lta (sqrt6-1)gta]` `therefore"Neglecting"x=a (-1-sqrt6)impliesx=a(sqrt6-1)" "...(ii)` From Eqs. (i) and (ii), we get `x={a(1-sqrt2),a (sqrt6-1)}` |
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