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Question Number 156176 by MathSh last updated on 08/Oct/21

Answered by ghimisi last updated on 09/Oct/21

$$\frac{a^2}{x^2}+\frac{1}{y^2}+\frac{c^2}{z^2}=36$$$${36\cdot 4=(\frac{a^2}{x^2}+\frac{1}{y^2}+\frac{c^2}{z^2})(x^2+b^2{y}^2+z^2)\stackrel{cbs}{⩾}(a+b+c))}^2=144\Rightarrow$$$$\frac{\frac{a}{x}}{x}=\frac{\frac{1}{y}}{by}=\frac{\frac{c}{z}}{z}\Rightarrow \frac{a}{x^2}=\frac{b}{b^2{y}^2}=\frac{c}{z^2}=\frac{12}{4}=3$$$$x^2=\frac{a}{3};y^2=\frac{1}{3b};z^2=\frac{c}{3}......$$

Commented by MathSh last updated on 09/Oct/21

$$\mathrm{Very}\mathrm{nice}\mathrm{solution}\mathrm{dear}\mathrm{Ser}\mathrm{thank}\mathrm{you}$$

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