A = x² +10x + 1

A = (x² + 2.5x + 25) - 24

A = (x+5)² - 24

( x + 5)² ≥ 0 ⇔ (x + 5)² - 24 ≥ -24 

A (min) = - 24 ⇔ x = -5

\(\left(\dfrac{2}{5}x-2\right):\left(\dfrac{-3}{2}\right)=\dfrac{1}{3}\\ \Leftrightarrow\dfrac{2}{5}x-2=\dfrac{1}{3}.\dfrac{-3}{2}\\ \Leftrightarrow\dfrac{2}{5}x-2=\dfrac{-1}{2}\\ \Leftrightarrow\dfrac{2}{5}x=\dfrac{-1}{2}+2=\dfrac{-3}{2}\\ \Rightarrow x=\dfrac{-3}{2}:\dfrac{2}{5}=\dfrac{-3}{2}.\dfrac{2}{5}=\dfrac{-3}{5}\)

(\(\dfrac{2}{5}x\) - 2 ) : ( -\(\dfrac{3}{2}\) ) =  \(\dfrac{1}{3}\)

\(\dfrac{2}{5}x\)  -  2  =  \(\dfrac{1}{3}\).\((-\dfrac{3}{2})\)

\(\dfrac{2}{5}x\) - 2 =  \(-\dfrac{1}{2}\)

\(\dfrac{2}{5}\)\(x\)   =   2 - \(\dfrac{1}{2}\)

\(\dfrac{2}{5}x\) = \(\dfrac{3}{2}\)

\(x\) = \(\dfrac{3}{2}\) : \(\dfrac{2}{5}\)

\(x\) = \(\dfrac{15}{4}\)

\(=\dfrac{3}{4}:\left(\dfrac{2\times9-5\times3}{27}\right)+\dfrac{9}{4}\\ =\dfrac{3}{4}:\dfrac{1}{9}+\dfrac{9}{4}\\ =\dfrac{27}{4}+\dfrac{9}{4}\\ =\dfrac{27+9}{4}=\dfrac{36}{4}=9\)

= 3/4 : ( 2/3 - 5/9 ) + 9/4

= 3/4 : ( 18/27 - 15/27 ) + 9/4

= 3/4 :  1/9 + 9/4

= 27/4  +  9/4

= 36/4

=  9        :33

    ( \(-\dfrac{1}{2}\))² - \(\dfrac{5}{8}\) : (0,5)³ - \(\dfrac{5}{3}\) .(-6)

=  \(\dfrac{1}{4}\)   -  \(\dfrac{5}{8}\) : (\(\dfrac{1}{2}\))³ - \(\dfrac{5}{3}\) .( -6)

=   \(\dfrac{1}{4}\)  -  \(\dfrac{5}{8}\) : \(\dfrac{1}{8}\)  + 10

=    \(\dfrac{1}{4}\) -  5 + 10

= \(\dfrac{1}{4}+5\)

= 21/4

    \(\dfrac{8}{9}-\dfrac{1}{72}-\dfrac{1}{56}-\dfrac{1}{42}-.....-\dfrac{1}{6}-\dfrac{1}{2}\)

= \(\dfrac{8}{9}-(\dfrac{1}{72}+\dfrac{1}{56}+\dfrac{1}{42}+.....+\dfrac{1}{6}+\dfrac{1}{2})\)

=  \(\dfrac{8}{9}\) - \((\)\(\dfrac{1}{9.8}+\dfrac{1}{8.7}+\dfrac{1}{7.6}+\dfrac{1}{6.5}+.....+\dfrac{1}{1.2}\) \()\)

= \(\dfrac{8}{9}\)  - \((\) \(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+.....+\dfrac{1}{8.9}\)\()\)

= \(\dfrac{8}{9}\) - (\(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+.....+\dfrac{1}{8}-\dfrac{1}{9}\)\()\)

= \(\dfrac{8}{9}\) - \((\) 1- \(\dfrac{1}{9}\))

= \(\dfrac{8}{9}\) - \(\dfrac{8}{9}\)

= 0