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Question Number 122579 by bramlexs22 last updated on 18/Nov/20

Answered by liberty last updated on 18/Nov/20

$$\left(2\mathrm{a}\right)\mathrm{Q}\mathrm{symetric}\mathrm{if}\mathrm{Q}={\mathrm{Q}}^{\mathrm{t}}$$$$\iff \left(\begin{array}{c}56\mathrm{x}+5\mathrm{y}1\\ 46{5\mathrm{y}}^2-2\mathrm{x}\\ {\mathrm{x}}^2-83\mathrm{z}\mathrm{p}\end{array}\right)=\left(\begin{array}{c}54{\mathrm{x}}^2-8\\ 6\mathrm{x}+5\mathrm{y}63\mathrm{z}\\ 1{5\mathrm{y}}^2-2\mathrm{x}\mathrm{p}\end{array}\right)$$$$\mathrm{gives}\{\begin{array}{l}6\mathrm{x}+5\mathrm{y}=1\wedge {\mathrm{x}}^2-8=1\{\begin{array}{l}\mathrm{x}=3\\ \mathrm{x}=-3\end{array}\\ \mathrm{y}=\{\begin{array}{l}\frac{1-6\left(3\right)}{5}=-\frac{17}{5}\\ \frac{1-6(-3)}{5}=\frac{19}{5}\end{array}\end{array}$$$$\iff \mathrm{z}=\frac{{5\mathrm{y}}^2-2\mathrm{x}}{3}=\{\begin{array}{l}\frac{5{(-\frac{17}{5})}^2-2.3}{3}\\ \frac{5{\left(\frac{19}{5}\right)}^2-2.(-3)}{3}\end{array}$$

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