Zadanie 3
a)
(\frac{1}{3})^{x-1}\leq27
3^{-(x-1)}\leq3^3
3^{1-x}\leq3^3
1-x\leq3
-x\leq2|*(-1)
zmiana znaku
x\geq-2
x\in \langle-2;+\infty)
b)
(0,5)^{x^2}*2^{2x+2}<\frac{1}{64}
(\frac{1}{2})^{x^2}*2^{2x+2}<(\frac{1}{2})^6
2^{-x^2}*2^{2x+2}<2^{-6}
2^{-x^2+2x+2}<2^{-6}
-x^2+2x+2<-6
-x^2+2x+8<0
a=-1, b=2, c=8
a<0 ramiona paraboli skierowane w dół
\Delta=b^2-4ac=4-4*(-1)*8=36
\sqrt\Delta=6
x_1=\frac{-b-\sqrt\Delta}{2a}=\frac{-2-6}{2*(-1)}=\frac{-8}{-2}=4
x_2=\frac{-b+\sqrt\Delta}{2a}=\frac{-2+6}{-2}=\frac{4}{-2}=-2
x\in (-\infty;-2)\cup (4;+\infty)