Question Number 134432 by liberty last updated on 03/Mar/21
![What is the maximum and minimum value of x^2 +y^2 +z^2 subject to (x^2 /4)+(y^2 /5)+(z^2 /(25)) = 1 and z = x+y .](https://www.tinkutara.com/question/Q134432.png)
$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{and}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} \:\mathrm{subject}\:\mathrm{to}\: \\ $$$$\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{4}}+\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{5}}+\frac{\mathrm{z}^{\mathrm{2}} }{\mathrm{25}}\:=\:\mathrm{1}\:\mathrm{and}\:\mathrm{z}\:=\:\mathrm{x}+\mathrm{y}\:. \\ $$