Question Number 142854 by liberty last updated on 06/Jun/21
$$\:\:{The}\:{maximum}\:{value}\:{of}\: \\ $$$$\:{y}=\sqrt{\left({x}−\mathrm{3}\right)^{\mathrm{2}} +\left({x}^{\mathrm{2}} −\mathrm{2}\right)^{\mathrm{2}} }−\sqrt{{x}^{\mathrm{2}} +\left({x}−\mathrm{1}\right)^{\mathrm{2}} }\: \\ $$$$\:{is}\: \\ $$
Commented by 1549442205PVT last updated on 06/Jun/21
$$\mathrm{Lim}\underset{\mathrm{x}\rightarrow\infty} {\mathrm{y}}=+\infty.\mathrm{Hence}\:\mathrm{there}\:\mathrm{isn}'\mathrm{t}\: \\ $$$$\mathrm{greatest}\:\mathrm{value}\:\mathrm{of}\:\mathrm{y} \\ $$