<s>[INST] Find the sum of all possible values of $a$ such that the following equation $(x - a)^2 + (x^2 - 3x + 2)^2 = 0$ has real root in $x$ :- 
Find the sum of all possible values of $a$ such that the following equation $(x - a)^2 + (x^2 - 3x + 2)^2 = 0$ has real root in $x$ :-

What I Tried :- I know $(x^2 - 3x + 2) = (x - 1)(x - 2)$ .
So :- $(x - a)^2 = - (x^2 - 3x + 2)^2$
=> $(x - a) = -(x^2 - 3x + 2)$
=> $(x - a) = -(x - 1)(x - 2) = (1 - x)(x - 2)$ .
From here I don't have a good hint or a clue to move forward . Can anyone help ?
 [/INST] Hint:sum of two non negative terms can be zero if they are both zero.
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