Question

Ma poate ajuta cineva? As dori o explicatie clara.
atasez o poza cu intrebarea.

Answer 1

Am atașat rezolvarea.

Answer 2

Explicație pas cu pas:

$4( {a}^{2} + {b}^{2} + {c}^{2}) = 4(3b + 5c - a) + 14$

$4{a}^{2} + 4a + 4{b}^{2} - 12b + 4{c}^{2} - 20c = 14$

${(2a)}^{2} + 2 \cdot 2a + 1 - 1 + {(2b)}^{2} - 2 \cdot 6b + 9 - 9 + {(2c)}^{2} - 2 \cdot 10c + 25 - 25 = 14$

${(2a + 1)}^{2} + {(2b - 3)}^{2} + {(2c - 5)}^{2} = 14 + 35$

$\underbrace{{(2a + 1)}^{2}}_{ \geqslant 0} + \underbrace{{(2b - 3)}^{2}}_{ \geqslant 0} + \underbrace{{(2c - 5)}^{2}}_{ \geqslant 0} = {7}^{2}$

$- 7 \leqslant 2a + 1 \leqslant 7 \iff - 8 \leqslant 2a \leqslant 6$

$- 4 \leqslant a \leqslant 3 \implies \bf a \in \Big[ - 4 ; 3\Big]$

$- 7 \leqslant 2b - 3 \leqslant 7 \iff - 4 \leqslant 2b \leqslant 10$

$- 2 \leqslant b \leqslant 5 \implies \bf b \in \Big[ - 2 ; 5\Big]$

$- 7 \leqslant 2c - 5 \leqslant 7 \iff - 2 \leqslant 2c \leqslant 12$

$- 1 \leqslant c \leqslant 6 \implies \bf c \in \Big[ - 1 ; 6\Big]$