Question

Решите неравенства
2^x+2^3-x<9​

Answer 1

$\displaystyle\bf\\2^{x} +2^{3-x} <9\\\\2^{x} +2^{3} \cdot2^{-x} -9<0\\\\2^{x}=m \ \ , \ \ m>0\\\\m+\frac{8}{m} -9<0\\\\\\\frac{m^{2} -9m+8}{m} <0\\\\\\\frac{(m-1)(m-8)}{m} <0$

0+ + + + + (1) - - - - - (8) + + + + +

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$\displaystyle\bf\\\left \{ {{m>1} \atop {m<8}} \right. \\\\\\\left \{ {{2^{x} >1} \atop {2^{x} <8}} \right. \\\\\\\left \{ {{2^{x} >2^{0} } \atop {2^{x} <2^{3} }} \right. \\\\\\\left \{ {{x>0} \atop {x<3}} \right. \\\\\\Otvet:x\in(0 \ ; \ 3)$