Question

Решите неравенства пожалуйста 

Answer 1

$1) 5^{-x} textgreater 625 \ \ 5^{-x} textgreater 5^4 \ \ -x textgreater 4 \ \ x textless -4$

$2) bigg (dfrac{1}{5} bigg )^{x^2 + x - 10} = 625 \ \ bigg (dfrac{1}{5} bigg )^{x^2 + x - 10} = bigg ( dfrac{1}{5} bigg )^{-4} \ \ x^2 + x - 10 = -4 \ \ x^2 + x - 6 = 0 \ \ x_1 + x_2 = -1\ x_1 cdot x_2 = -6 \ \ x_1 = -3 \ x_2 = 2$

$3) 7^{x^2 - x + 3} leq bigg ( dfrac{1}{7} bigg ) ^{5x} \ \ 7^{x^2 - x + 3} leq 7^{-5x} \ \ x^2 - x + 3 leq -5x \ \ x^2 + 4x + 3 leq 0 \ \ x^2 + 4x + 4 - 1 leq 0 \ \ (x + 2)^2 - 1^2 leq 0 \ \ (x + 2 - 1)(x + 2 + 1) leq 0 \ \ (x + 1)(x + 3) leq 0 \ \ x in [-3; -1]$

$4) 9^x cdot 27^y = 27 \ 2^x/4^y = 32 \ \ 3^{2x} cdot 3^{3y} = 3^{3} \ 2^{x}/2^{2y} = 2^5 \ \ 3^{2x + 3y} = 3^{3} \ 2^{x - 2y} = 2^{5} \ \ 2x + 3y = 3 \ x - 2y = 5 \ \ 2x + 3y = 3 \ 2x - 4y = 10 \ \ 7y = -7 \ \ y = -1 \ 2x - 3 = 3 \ \ y = -1 \ 2x = 6 \ \ y = -1 \ x = 3 \ \ OTBET: (3; -1).$