Question

va rog ex 1 !!!!!!!!!!!!!

Answer 1

$\bold{a)} \ 2^2-(-3)^2\cdot [-3^3:9+45^{2010}\cdot (2010^0-2011^0)]^2:3^3=\\=4-9\cdot (-27:9+45^{2010}\cdot 0)^2:3^3= \\ =4-9(-3+0)^2:27= \\ =4-9\cdot 9:27=\\=4-81:27=\\=4-3=\boxed{1}$

$\bold{b)} \ (\frac{5}{4})^2:\frac{5}{4}-(\frac{3}{2})^2+(\frac{1}{2})^3=\frac{5}{4}-(\frac{9}{4}+\frac{1}{8})= \frac{5}{4}-\frac{36+2}{16}= \\ =\frac{5}{4}-\frac{38}{16}=\frac{5}{4}-\frac{19}{8}=\frac{20-38}{16}=-\frac{18}{16}=\boxed{-\frac{9}{8}}$

$\bold{c)} \ \frac{3x-1}{2}=\frac{x+2}{3} \Leftrightarrow 3(3x-1)=2(x+2) \\ 9x-3=2x+4 \\ 9x=2x+7 \\ 7=9x-2x=7x \\ \Rightarrow \boxed{x=1};$