Question

(3^{x^2}) / (27^x)=<81

Answer 1

$\frac{3 ^{ x^{2} } }{27 ^{x} } \leq 81 \\ \\ \frac{3 ^{ x^{2} } }{3 ^{3x} } \leq 3 ^{4} \\ \\ a=3\ \textgreater \ 1 \\ \\ x^{2} -3x \leq 4$

$x^{2} -3x-4 \leq 0 \\ x^{2} -3x-4=0\\D=9+16=25 \\ \sqrt{D} =5 \\ x_{1} = \frac{3+5}{2} = \frac{8}{2} =4 \\ x_{2} = \frac{3-5}{2} =- \frac{2}{2} =-1 \\ \\ x\in[-1;4]$

Answer 2

$\frac{ 3^{ x^{2} } }{ 3^{3x} } \leq 3^{4}$
$x^{2} -3x \leq 4$
$x^{2} -3x-4 \leq 0$
x²-3x-4=0
по теореме виета 
х1+х2=3
х1*х2=-4
х1=-1
х2=4

ветви направлены в верх 
х∈[-1 ,   4]