Question

Допоможіть будь ласка

Answer 1

Ответ: x∈[-1;3].

Объяснение:

$\displaystyle\\0,5^{2x-3}-17*0,5^x+2\leq 0\\\\\frac{0,5^{2x}}{0,5^3} -17*0,5^x+2\leq 0\\\\\frac{0,5^{2x}}{0,125} -17*0,5^x+2\leq 0\\\\8*0,5^{2x}-17*0,5^x+2\leq 0$

Пусть 0,5ˣ=t>0        ⇒

$8t^2-17t+2\leq 0\\\\8t^2-16t-t+2\leq 0\\\\8t*(t-2)-(t-2)\leq 0\\\\(t-2)*(8t-1)\leq 0\\\\t-2=0\\\\t=0,5^x=2=0,5^{-1}\\\\x_1=-1.\\\\8t-1=0\\\\8t=1\ |:8\\\\t=0,5^x=0,125=(0,5)^3\\\\x_2=3.$

-∞__+__-1__-__3__+__+∞       ⇒             x∈[-1;3].