InterviewSolution
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InterviewSolution
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The sum of all the real roots of the equation `|x-2|^2+|x-2|-2=0` is |
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Answer» Correct Answer - 4 Given, `|x-2|^(2)+|x-2|-2=0` Case I When `c ge 2` `implies(x-2)^(2)+(x-2)-2=0` `impliesx^(2)+4-4x+x-2-2=0` `impliesx^(2)-3x=0` `impliesx(x-3)=0` `impliesx=0,3" "[0 "is rejected"]` `impliesx=3" "...(i)` Case II When `x gt 2` `implies{-(x-2))^(2)-(x-2)-3=0` `(x-2)^(2)-x+2-2=0` `impliesx^(2)+4-4x-x=0` `impliesx^(2)--4x-(x-4)=0` `impliesx(x-4)-1(x-4)=0` `implies(x-1)(x-4)=0` `impliesx=1,4" "["4 is rejected"]` `impliesx=1" "...(ii)` Hence, the sum of the roots is `3+1 =4.` Alternate Solution Given, `|x-2|^(2)+|x2|2=0` `implies(|x-2|+2)(|x-2|-1)=0` `therefore|x-2|=-2,1" "["neglacting"-2]` `implies|x-2|=1impliesx=3,1` `implies` Sum of the roots `=4` |
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