120/MR00. zadatak / Matematika - Zbirka rešenih zadataka

MR-120. zadatak

Izračunati vrednost sledećeg izraza:

${[6 - 4 {(\frac{7}{16})}^{0}]}^{- 2} + {(\frac{2}{3})}^{- 1} + \frac{1}{4}$

${[6 - 4 {(\frac{7}{16})}^{0}]}^{- 2} + {(\frac{2}{3})}^{- 1} + \frac{1}{4}$

$= {(6 - 4 \cdot 1)}^{- 2} + {(\frac{3}{2})}^{1} + \frac{1}{4}$

$= 2^{- 2} + \frac{3}{2} + \frac{1}{4}$

$= \frac{1}{2^{2}} + \frac{3}{2} + \frac{1}{4}$

$= \frac{1}{4} + \frac{3}{2} + \frac{1}{4}$

$= \frac{1 + 2 \cdot 3 + 1}{4}$

$= \frac{1 + 6 + 1}{4}$

$= \frac{8}{4}$

$= 2$

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