Question

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

Answer 1

$16x^4-25x^2+9=0;\ x^2=t;\ tgeq0;\ 16t^2-25t+9=0;\ D=b^2-4cdot acdot c=(-25)^2-4cdot16cdot9=625-576=49=(pm7)^2;\ t_1=frac{-b-sqrt D}{2cdot a}=frac{25-7}{2cdot32}=frac{18}{64}; x_1_2=pmsqrt{t_1};\ t_2=frac{-b+sqrt D}{2cdot a}=frac{25+7}{2cdot32}=frac{32}{2cdot32}=frac12; x_34=pmsqrt{t_2};\ x_1=frac{3sqrt2}{8};\ x_2=-frac{3sqrt2}{8};\ x_3=frac{1}{sqrt2};\ x_4=-frac{1}{sqrt2}.$