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The sum of all real roots of the equation $|x-2|^2+|x-2|-2=0$
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2775 Upvotes
Verified Answer
The correct answer is:
4
Hints: Put $1 x-21=y$
$$
\begin{aligned}
& y^2+y-2=0 \\
& (y-1)(y+2)=0 \\
& y=1 \\
& |x-2|=1 \\
& x-2= \pm 1 \\
& x=2 \pm 1 \\
& x=3,1
\end{aligned}
$$
$$
y=-2
$$
(Not possible)
Sum $=4$
$$
\begin{aligned}
& y^2+y-2=0 \\
& (y-1)(y+2)=0 \\
& y=1 \\
& |x-2|=1 \\
& x-2= \pm 1 \\
& x=2 \pm 1 \\
& x=3,1
\end{aligned}
$$
$$
y=-2
$$
(Not possible)
Sum $=4$
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