Question

Решите уравнение пожалуйста срочно

Answer 1

${3}^{ {x}^{2} + 4x } + {3}^{3 - {x}^{2} } < 28 times {3}^{2x} \ \ { {(3}^{2x} )}^{2} times {3}^{ {x}^{2} } + frac{27}{ {3}^{ {x}^{2} } } < 28 times {3}^{2x}$

Сделаем замену:

$a = {3}^{2x} \ \ b = {3}^{ {x}^{2} }$


${a}^{2} b + frac{27}{b} < 28a \ \ {a}^{2} {b}^{2} - 28ab + 27 < 0$

Решим относительно а

D = ( -28b)² - 4×1×27×b² = 676b²

$a = frac{28b + - 26b}{2 {b}^{2} } \ \1) : a = frac{1}{b } \2) : a = frac{27}{b}$

Обратная замена:

$1) : a = frac{1}{b} \ {3}^{2x} = frac{1}{ {3}^{ {x}^{2} } } \ {3}^{2x} = {3}^{ - {x}^{2} } \ 2x = - {x}^{2} \ {x}^{2} + 2x = 0 \ x times (x + 2) = 0 \ x = 0 \ x = - 2$

$2) : a = frac{27}{b} \ \ {3}^{2x} = frac{27}{ {3}^{ {x}^{2} } } \ {3}^{2x} = {3}^{3 - {x}^{2} } \ 2x = 3 - {x}^{2} \ {x}^{2} + 2x - 3 = 0 \ x = - 3 \ x = 1$


ОТВЕТ:
$x = - 3 \ x = - 2 \ x = 0 \ x = 1$