Question

решите данные неравенства
(2-5x)^2>0

Answer 1

$(2-5x)^2>0,\4-10x-25x^2>0 |:(-1),\25x^2+10x-4<0,\\25x^2+10x-4=0,\D=10^2-4bullet25bullet(-4)=100+400=500,\\x_1=frac{-10+sqrt{500}}{2bullet25}=frac{-10+10sqrt5}{50}=frac{-1+sqrt5}{5},\x_2=frac{-1-sqrt5}{5}.\\25(x-frac{-1+sqrt5}{5})(x-frac{-1-sqrt5}{5})<0,\\frac{-1-sqrt5}{5}<x<frac{-1+sqrt5}{5}.$

Ответ: $xin (frac{-1-sqrt5}{5}; frac{-1+sqrt5}{5}).$