Question

Se considera numarul rational x = 2 intregi 1/4 ori [2 - 2,(4)/1.8(3) : 0.5]^3 - 5/6

Aratati ca x = - 1 intreg 1/2

Answer 1

[tex]\it 2\dfrac{1}{4} =\dfrac{9}{4} \\\;\\ \\\;\\ 2,(4) =2\dfrac{4}{9} =\dfrac{22}{9} \\\;\\ \\\;\\ 1,8(3) =1\dfrac{83-8}{90} =1\dfrac{75^{(15}}{90} =1\dfrac{5}{6} =\dfrac{11}{6} \\\;\\ \\\;\\ 0,5 = \dfrac{1}{2}[/tex]

[tex]\it x = \dfrac{9}{4}\left(2-\dfrac{22}{9}:\dfrac{6}{11}:\dfrac{1}{2}\right)^3-\dfrac{5} {6} = \dfrac{9}{4}\left(2-\dfrac{22}{9}\cdot\dfrac{6}{11}\cdot\dfrac{2}{1}\right)^3-\dfrac{5} {6} = \\\;\\ \\\;\\ = \dfrac{9}{4}\left(2-\dfrac{8}{3}\right)^3-\dfrac{5} {6} = \dfrac{9}{4}\left(-\dfrac{2}{3}\right)^3-\dfrac{5}{6}=\dfrac{9}{4}\cdot\left(-\dfrac{8}{27}\right)-\dfrac{5}{6} = \\\;\\ \\\;\\ = -\dfrac{4}{6}-\dfrac{5}{6} = -\dfrac{ \ 9^{(3}}{6} = - \dfrac{3}{2} = -1\dfrac{1}{2}[/tex]