Question Number 167718 by mathlove last updated on 23/Mar/22
$$\left({x}−\mathrm{3}\right)^{\mathrm{2}} +\left({y}−\mathrm{5}\right)^{\mathrm{2}} +\left({z}−\mathrm{4}\right)^{\mathrm{2}} =\mathrm{0} \\ $$$$\frac{{x}^{\mathrm{2}} }{\mathrm{9}}+\frac{{y}^{\mathrm{2}} }{\mathrm{25}}+\frac{{z}^{\mathrm{2}} }{\mathrm{16}}=? \\ $$$${help}\:{me} \\ $$
Commented by MJS_new last updated on 23/Mar/22
$$\mathrm{this}\:\mathrm{is}\:\mathrm{easy}\:\mathrm{because}\:\mathrm{all}\:\mathrm{squares}\:\mathrm{are}\:\geqslant\mathrm{0}\:\Rightarrow \\ $$$$\mathrm{if}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{squares}\:\mathrm{equals}\:\mathrm{0}\:\mathrm{each}\:\mathrm{square} \\ $$$$\mathrm{must}\:\mathrm{equal}\:\mathrm{0} \\ $$$$\Rightarrow \\ $$$${x}=\mathrm{3} \\ $$$${y}=\mathrm{5} \\ $$$${z}=\mathrm{4} \\ $$
Commented by alephzero last updated on 23/Mar/22
$$\Rightarrow\frac{{x}^{\mathrm{2}} }{\mathrm{9}}+\frac{{y}^{\mathrm{2}} }{\mathrm{25}}+\frac{{z}^{\mathrm{2}} }{\mathrm{16}}=\frac{\mathrm{3}^{\mathrm{2}} }{\mathrm{9}}+\frac{\mathrm{5}^{\mathrm{2}} }{\mathrm{25}}+\frac{\mathrm{4}^{\mathrm{2}} }{\mathrm{16}}=\mathrm{3} \\ $$