Question

Rezolvați următoarele sisteme de ecuații ex 31 dau 50 puncte!!!

Answer 1

Am atasat poza cu rezolvarile

Answer 2

Răspuns:

$x = \sqrt{2} ;y = \sqrt{3} \\ x = \sqrt{5} ;y = - \sqrt{3} \\ x = \sqrt{6} ;y = 2$

Explicație pas cu pas:

$\sqrt{2} x + \sqrt{3} y + 2y = 2y + 4 + 1 \\ \sqrt{8} x + 2x - \sqrt{12}y = 4 + 2x - 6 \\ \\ \sqrt{2}x + \sqrt{3} y = 5 | \times (2)| \\ 2 \sqrt{2} x - 2 \sqrt{3}y = - 2 \\ \\ 2 \sqrt{2} x + 2 \sqrt{3} y = 10 \\ 2 \sqrt{2} x - 2 \sqrt{3}y = - 2 \\ \\ 4 \sqrt{2} x = 8 \\ x = \frac{8}{4 \sqrt{2} } = \frac{2}{ \sqrt{2} } = \sqrt{2} \\ \sqrt{3}y = 5 - \sqrt{2} \times \sqrt{2} = 5 - 2 = 3 \\ y = \frac{3}{ \sqrt{3} } = \sqrt{3}$

$2 \sqrt{5} x + 4x + 3 \sqrt{3} y = 4x + 4 - 3 \\ 4 \sqrt{5}x - 4 \sqrt{3}y + 5y = 30 + 5y + 2\\ \\ 2 \sqrt{5} x + 3 \sqrt{3} y = 1 | \times ( - 2)| \\ 4 \sqrt{5}x - 4 \sqrt{3}y = 32 \\ \\ - 4 \sqrt{5} x - 6 \sqrt{3} y = - 2 \\ 4 \sqrt{5}x - 4 \sqrt{3}y = 32 \\ \\ - 10 \sqrt{3} y = 30 \\ y = - \frac{30}{10 \sqrt{3} } = - \frac{3}{ \sqrt{3} } = - \sqrt{3} \\ 2 \sqrt{5} x = 1 - 3 \sqrt{3} \times ( - \sqrt{3} ) = 1 + 9 = 10 \\ x = \frac{10}{2 \sqrt{5} } = \frac{5}{ \sqrt{5} } = \sqrt{5}$

$3 \sqrt{6} x + \sqrt{3} y - 2y = 2 \sqrt{3} + 6y + 2 \\ 4 \sqrt{6} x - 3x + 4y = 2 + 30 - 3x \\ \\ 3 \sqrt{6} x + \sqrt{3} y - 8y = 2 \sqrt{3} + 2 | \times( - 4) | \\ 4 \sqrt{6} x + 4y = 32 | \times (3)| \\ \\ - 12 \sqrt{6} x - 4\sqrt{3} y + 32y = - 8\sqrt{3} - 8 \\ 12 \sqrt{6} x + 12y = 96 \\ \\ - 4\sqrt{3} y + 44y = - 8\sqrt{3} + 88 \\ y \times 4(11 - \sqrt{3}) = 8(11 - \sqrt{3}) \\ y = 2 \\ 4 \sqrt{6} x = 32 - 8 = 24 \\ x = \frac{24}{4 \sqrt{6} } = \frac{6}{ \sqrt{6} } = \sqrt{6}$