Question

помогите пожалуйстааа

Answer 1

$\frac{2\cdot 9^{a}-3\cdot 15^{a}-25^{a}}{2\cdot 9^{a}-7\cdot 15^{a}-3\cdot 25^{a}}=\frac{2\cdot 3^{2a}-3\cdot 3^{a}\cdot 5^{a}-5^{2a}}{2\cdot 3^{2a}-7\cdot 3^{a}\cdot 5^{a}-3\cdot 5^{2a}}=\frac{3^{2a}\cdot \; (2-3\cdot (\frac{5}{3})^{a}-(\frac{5}{3})^{2a})}{3^{2a}\cdot \; (2-7\cdot (\frac{5}{3})^{a}-3\cdot (\frac{5}{3})^{2a})}=\\\\=[\, t=(\frac{5}{3})^{a}>0\; ]=\frac{2-3t-t^2}{2-7t-3t^2}=\frac{t^2+3t-2}{3t^2+7t-2}=\frac{1}{4}\; \; \Rightarrow \\\\4(t^2+3t-2)=3t^2+7t-2\\\\4t^2+12t-8-3t^2-7t+2=0\\\\t^2+5t-6=0$

$t_1=-6\; ,\; \; t_2=1\; \; (teorema\; Vieta)\\\\(\frac{5}{3})^{a}=-6<0\; \; ne\; \; podxodit\\\\(\frac{5}{3})^{a}=1\; \; \Rightarrow \; \; \; \frac{5^{a}}{3^{a}}=1$