Question

Решить неравенство: (2/7)^(3(x-(1/3)))<(4/49)^x²

Answer 1

$(frac{2}{7})^{3(x-frac{1}{3})} textless (frac{4}{49})^{x^2}\(frac{2}{7})^{3x-1} textless (frac{2}{7})^{2x^2}\3x-1 textgreater 2x^2\2x^2-3x+1 textless 0\D=9-8=1\x_{1,2}=frac{-bбsqrt{D}}{2a}=frac{3б1}{4}toleft[begin{array}{ccc}x_1=frac{3+1}{4}=1\x_2=frac{3-1}{4}=frac{1}{2}end{array}right\boxed{frac{1}{2} textless x textless 1}$

ответ: x∈(0,5; 1)