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What-is-the-he-minimum-value-of-x-2-1-y-x-2-25-z-y-2-4-9-z-2-16-if-x-y-and-z-R-




Question Number 110799 by dw last updated on 30/Aug/20
                    What is the he minimum value of              (√(x^2 +1))+(√((y−x)^2 +25))+(√((z−y)^2 +4))+(√((9−z)^2 +16))                 if  (x, y and z) ∈ R
$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{What}\:{is}\:{the}\:{he}\:{minimum}\:{value}\:{of}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}+\sqrt{\left({y}−{x}\right)^{\mathrm{2}} +\mathrm{25}}+\sqrt{\left({z}−{y}\right)^{\mathrm{2}} +\mathrm{4}}+\sqrt{\left(\mathrm{9}−{z}\right)^{\mathrm{2}} +\mathrm{16}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{if}\:\:\left({x},\:{y}\:{and}\:{z}\right)\:\in\:\mathbb{R}\: \\ $$

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