Question

алгебра помогите плез

Answer 1

$2x^2-5x-4=0\; \; \Rightarrow \; \; \left \{ {{x_1+x_2=\frac{5}{2}} \atop {x_1\cdot x_2=-\frac{4}{2}}} \right. \; \; \left \{ {{x_1+x_2=2,5} \atop {x_1\cdot x_2=-2}} \right.\; \left \{ {{(x_1+x_2)^2=6,25} \atop {x_1\cdot x_2=-2}} \right. \\\\\left \{ {{x_1^2+x_2^2+2x_1x_2=6,25} \atop {x_1\cdot x_2=-2}} \right. \; \left \{ {{x_1^2+x_2^2=6,25-2\cdot (-2)} \atop {x_1\cdot x_2=-2}} \right. \; \left \{ {{x_1^2+x_2^2=10,25} \atop {x_1\cdot x_2=-2}} \right. \\\\1)\; \; \frac{1}{x_1^2}+\frac{1}{x_2^2}=\frac{x_1^2+x_2^2}{x_1^2\cdot x_2^2}=\frac{10,25}{(-2)^2}=\frac{10,25}{4}=2,5625$

$2)\; \; x_1x_2^4+x_2x_1^4=x_1x_2\cdot (x_2^3+x_1^3)=\\\\=x_1x_2\cdot (x_1+x_2)\cdot (x_1^2-x_1x_2+x_2^2)=-2\cdot 2,5\cdot \Big (10,25-(-2)\Big )=\\\\=-5\cdot 12,25=-61,25$