Question

Решите уравнение: 16х4 − 25х2 + 9 = 0.

Answer 1

$16x^4-25x^2+9=0;\\ x^2=t;\\ t\geq0;\\ 16t^2-25t+9=0;\\ D=b^2-4\cdot a\cdot c=(-25)^2-4\cdot16\cdot9=625-576=49=(\pm7)^2;\\ t_1=\frac{-b-\sqrt D}{2\cdot a}=\frac{25-7}{2\cdot32}=\frac{18}{64}; x_1_2=\pm\sqrt{t_1};\\ t_2=\frac{-b+\sqrt D}{2\cdot a}=\frac{25+7}{2\cdot32}=\frac{32}{2\cdot32}=\frac12;\ x_34=\pm\sqrt{t_2};\\ x_1=\frac{3\sqrt2}{8};\\ x_2=-\frac{3\sqrt2}{8};\\ x_3=\frac{1}{\sqrt2};\\ x_4=-\frac{1}{\sqrt2}.$