Giải phương trình và hệ phương trinh sau:

$\begin{array}{l}a)x^2-3x-7=0\\ b)4x^2-12x+9=0\\ c)2x^2-5x+7=0\\ d)\left\{\begin{array}{l}{x}^2+x\left(y-3\right)+2-y=0\\ x^2+y^2=2\end{array}\right.\end{array}$

$a)x^2-3x-7=0$có : $\Delta =37$nên phương trình có hai nghiệm : $x=\frac{3\pm \sqrt{37}}{2}$

$b)4x^2-12x+9=0\iff {\left(2x-3\right)}^2=0\iff x=\frac{3}{2}$

$c)2x^2-5x+7=0$ có $\Delta =-31<0\Rightarrow$phương trình vô nghiệm.

$d)\left\{\begin{array}{l}{x}^2+x\left(y-3\right)+2-y=0\left(1\right)\\ x^2+y^2=2\end{array}\right.$

$\begin{array}{l}\left(1\right)\iff x^2+x\left(y-3\right)+3-y-1=0\\ \iff \left(x^2-1\right)+\left(y-3\right)\left(x-1\right)=0\\ \iff \left(x-1\right)\left(x+1+y-3\right)=0\iff \left[\begin{array}{l}x=1\\ y=2-x\end{array}\right.\end{array}$

$*)x=1\Rightarrow y^2=1\Rightarrow y=\pm 1$

$*)y=2-x\Rightarrow x^2+{\left(2-x\right)}^2=2\iff 2x^2-4x+2=0\iff x=1\Rightarrow y=1$

Vậy $\left(x;y\right)\in \left\{\left(1;1\right);\left(1;-1\right)\right\}$