Объяснение:
[tex]x^2+4x-3=0\ \ \ \ \frac{1}{x_1^2}+\frac{1}{x_2^2}=?\\ -(x_1+x_2)=4\ |*(-1)\\ x_1+x_2=-4.\\x_1*x_2=-3.\\\frac{1}{x_1^2}+\frac{1}{x_2^2}=\frac{x_2^2+x_1^2}{x_1^2*x_2^2}=\frac{x_1^2+2*x_1*x_2+x_2^2 -2*x_1*x_2}{(x_1*x_2)^2}=\frac{(x_1+x_2)^2-2*x_1*x_2}{(x_1*x_2)^2}=\\=\frac{(-4)^2-2*(-3)}{(-3)^2}=\frac{16+6}{9}=\frac{22}{9} . \\OTBET: \frac{1}{x_1^2}+\frac{1}{x_2^2}=\frac{22}{9}.[/tex]
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Объяснение:
[tex]x^2+4x-3=0\ \ \ \ \frac{1}{x_1^2}+\frac{1}{x_2^2}=?\\ -(x_1+x_2)=4\ |*(-1)\\ x_1+x_2=-4.\\x_1*x_2=-3.\\\frac{1}{x_1^2}+\frac{1}{x_2^2}=\frac{x_2^2+x_1^2}{x_1^2*x_2^2}=\frac{x_1^2+2*x_1*x_2+x_2^2 -2*x_1*x_2}{(x_1*x_2)^2}=\frac{(x_1+x_2)^2-2*x_1*x_2}{(x_1*x_2)^2}=\\=\frac{(-4)^2-2*(-3)}{(-3)^2}=\frac{16+6}{9}=\frac{22}{9} . \\OTBET: \frac{1}{x_1^2}+\frac{1}{x_2^2}=\frac{22}{9}.[/tex]