Question

sisteme de ecuatii cu 2 necunoscute
va rog! Ma incurc la ecuatiile cu radicali!​

Answer 1

Răspuns:

Explicație pas cu pas:

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Answer 2

$\it Vom\ elimina\ parantezele, \ prin\ efectuarea\ \hat\imath nmul\c{\it t}irilor\ .$

$\it \begin{cases} \it x(\sqrt3+2)+\sqrt{18}y = 2(x-6) \\ \\ \it \sqrt{12}x+y(\sqrt2+3)=3(y+2)\end{cases}\ \Leftrightarrow \begin{cases} \it \sqrt3 x+2x+3\sqrt2y = 2x-12 \\ \\ \it 3\sqrt2x+\sqrt2y+3y=3y+6\end{cases}\ \Leftrightarrow$

$\it \begin{cases} \it \sqrt3x+3\sqrt2y = -12 \\ \\ \it 2\sqrt3x+\sqrt2 y=6\bigg|_{\cdot(-3)}\end{cases}\ \Leftrightarrow\ \begin{cases} \it \sqrt3x\ +\ 3\sqrt2y \ = -12 \\ \\ \it -6\sqrt3x-3\sqrt2 y=-18\end{cases}\\ \rule{0.2}{0.2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \rule{120}{0.7}\\ \rule{0.2}{0.2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -5\sqrt3 x \ \ \ \ \ \ = -30$

$\it -5\sqrt3x=-30\bigg|_{:(-5)} \Rightarrow \sqrt3x=6 \Rightarrow x=\dfrac{^{\sqrt3)}6}{\ \ \sqrt3}=\dfrac{6\sqrt3}{3}=2\sqrt3$

$\it 2\sqrt3x+\sqrt2 y=6\ \ \d s i\ \ x=2\sqrt3\ \Rightarrow 12+\sqrt2y=6\bigg|_{-12} \Rightarrow \sqrt2y=-6\Rightarrow \\ \\ \\ \Rightarrow y=-\dfrac{6}{\sqrt2}=-\dfrac{6\sqrt2}{2}=-3\sqrt2\\ \\ \\ S:\begin{cases} \it x=2\sqrt3\\ \\ \it y=-3\sqrt2\end{cases}$