<s>[INST] Finding minimum $\sqrt{x^2-3x+3}+\sqrt{x^2-3x+2}$ I would appreciate if somebody could help me with the following problem
Q. Finding minimum $f(x)$
$$f(x)=\sqrt{x^2-3x+3}+\sqrt{x^2-3x+2}$$
 [/INST] Hint: Since
$$f(x)=\sqrt{x^2-3x+3}+\sqrt{x^2-3x+2} = \sqrt{\left(x-\dfrac32\right)^2 + \dfrac34} + \sqrt{\left(x-\dfrac32\right)^2 - \dfrac14},$$
we have $\left(x-\dfrac32\right)^2 + \dfrac34 \ge \dfrac14+\dfrac34 = 1$.
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