Question

URGENT!Ofer 100 de puncte.

Answer 1

Explicație pas cu pas:

a)

$= {x}^{2} - 2 \cdot x \cdot 2 + {2}^{2} + {y}^{2} + 2 \cdot y \cdot 3 + {3}^{2}$

$= {(x - 2)}^{2} + {(y + 3)}^{2}$

b)

$= {x}^{2} + 2 \cdot x + {1}^{2} + {y}^{2} - 2 \cdot 5x + {5}^{2}$

$= {(x + 1)}^{2} + {(y - 5)}^{2}$

c)

$= {x}^{2} + 2 \cdot x \cdot 3 + {3}^{2} + {y}^{2} + 2 \cdot y \cdot 6 + {6}^{2}$

$= {(x + 3)}^{2} + {(y + 6)}^{2}$

d)

$= {x}^{2} - 2 \cdot x \cdot 1 + {1}^{2} + {(2y)}^{2} - 2 \cdot 2y \cdot 3 + {3}^{2}$

$= {(x - 1)}^{2} + {(2y + 3)}^{2}$

e)

$= {(5x)}^{2} + 2 \cdot 5x \cdot 2 + {2}^{2} + {(6y)}^{2} - 2 \cdot 6y \cdot 3 + {3}^{2}$

$= {(5x + 2)}^{2} + {(6y - 3)}^{2}$

$= {(5x + 2)}^{2} + 9{(2y - 1)}^{2}$

f)

$= {x}^{2} + 2 \cdot x \cdot \dfrac{3}{2} + { \bigg( \dfrac{3}{2} \bigg)}^{2} + {y}^{2} - 2 \cdot y \cdot \dfrac{ \sqrt{3} }{2} + { \bigg( \dfrac{ \sqrt{3} }{2} \bigg)}^{2}$

$= { \bigg(x + \dfrac{3}{2} \bigg)}^{2} + { \bigg(y - \dfrac{ \sqrt{3} }{2} \bigg)}^{2}$