Spośród podanych par liczb podkreśl te, dla ... - Zadanie 2: Matematyka 6

Rozwiązanie

a = 8, b = 3

Mamy więc:

$\frac{3 a ^{2} - 4 a b}{5} = \frac{3 \cdot 8 ^{2} - 4 \cdot 8 \cdot 3}{5} = \frac{3 \cdot 64 - 32 \cdot 3}{5} = \frac{192 - 96}{5} = \frac{96}{5} = 19 \frac{1}{5} \neq = 23$

a = 3, b = -1

Mamy więc:

$\frac{3 a ^{2} - 4 a b}{5} = \frac{3 \cdot 3 ^{2} - 4 \cdot 3 \cdot ( - 1 )}{5} = \frac{3 \cdot 9 - 12 \cdot ( - 1 )}{5} = \frac{27 + 12}{5} = \frac{39}{5} = 7 \frac{4}{5} \neq = 23$

a = -5, b = 2

Mamy więc:

$\frac{3 a ^{2} - 4 a b}{5} = \frac{3 \cdot ( - 5 ) ^{2} - 4 \cdot ( - 5 ) \cdot 2}{5} = \frac{3 \cdot 25 + 20 \cdot 2}{5} = \frac{75 + 40}{5} = \frac{115}{5} = 23$

a = 5, b = -2

Mamy więc:

$\frac{3 a ^{2} - 4 a b}{5} = \frac{3 \cdot 5 ^{2} - 4 \cdot 5 \cdot ( - 2 )}{5} = \frac{3 \cdot 25 - 20 \cdot ( - 2 )}{5} = \frac{75 + 40}{5} = \frac{115}{5} = 23$