Pismeni zadaci

Zadatak 0695

Test: MKo8BGII_140

 

Da li je tačna nejednakost: $$\frac{2}{5}\cdot \frac{1-(-2)^2}{3}+0,2:5>1+\left ( -\frac{1}{2} \right )^3$$

 

Rešenje:


$$\frac{2}{5}\cdot \frac{1-(-2)^2}{3}+0,2:5>1+\left ( -\frac{1}{2} \right )^3$$

$$\Leftrightarrow \frac{2}{5}\cdot \frac{1-4}{3}+\frac{1}{5}\cdot \frac{1}{5}>1 -\frac{1}{8} $$

$$\Leftrightarrow \frac{2}{5}\cdot (-1)+\frac{1}{25}>\frac{7}{8}$$

$$\Leftrightarrow -\frac{2}{5}+\frac{1}{25}>\frac{7}{8}$$

$$\Leftrightarrow -\frac{10}{25}+\frac{1}{25}>\frac{7}{8}$$

$$\Leftrightarrow -\frac{9}{25}>\frac{7}{8}\; !$$

Nejednakost nije tačna.