Може ли малко помощ?

[Гост]

20240406_144813.jpg (525.76 KiB) Прегледано 2199 пъти

[ammornil]

[tex]AC=b, \quad BC=a, \quad AB=c=9[cm], \quad h_{c}=4[cm] \\ S_{ABC}=\frac{1}{2}\cdot{a}\cdot{b}=\frac{1}{2}\cdot{c}\cdot{h_{c}} \Rightarrow a\cdot{b}=c\cdot{h_{c}} \Rightarrow a=\frac{c\cdot{h_{c}}}{b} \\ c^{2}=a^{2}+b^{2} \Leftrightarrow c^{2}=\left(\frac{c\cdot{h_{c}}}{b}\right)^{2}+b^{2} \Leftrightarrow b^{4}-c^{2}b^{2}+c^{2}h^{2}_{c}=0\\b^{4}-c^{2}b^{2}+c^{2}h^{2}_{c}=0 \Leftrightarrow \\ \quad D=c^{4}-4\cdot{c^{2}h^{2}_{c}}=c^{2}(c^{2}-4h^{2}_{c}) \\ b_{1,2}=\frac{c^{2}\pm c\sqrt{c^{2}-4h^{2}_{c}}}{2} \Rightarrow a_{1,2}=\frac{2h_{c}}{c\pm \sqrt{c^{2}-4h^{2}_{c}}}[/tex]