Question

Составьте квадратные уравнения с корнями

Answer 1

$1)x_{1} +x_{2}=\sqrt{3}+\sqrt{7}\\\\x_{1}*x_{2}=\sqrt{3}*\sqrt{7}=\sqrt{21}\\\\x^{2} -(\sqrt{3} +\sqrt{7})x+\sqrt{21}=0$

$2)x_{1} +x_{2}=-\sqrt{5}+\sqrt{2}\\\\x_{1}*x_{2}=-\sqrt{5}*\sqrt{2}=-\sqrt{10}\\\\x^{2}-(\sqrt{2}-\sqrt{5})x-\sqrt{10}=0$

$3)x_{1}+x_{2}=3-\sqrt{7}+2\sqrt{7}=3+\sqrt{7}\\\\x_{1}*x_{2}=(3-\sqrt{7})*2\sqrt{7}=6\sqrt{7}-14\\\\x^{2}-(3+\sqrt{7})x+6\sqrt{7}-14=0$

$4)x_{1}+x_{2}=-1-\sqrt{7}-1+\sqrt{7}=-2\\\\x_{1}*x_{2}=(-1-\sqrt{7})(-1+\sqrt{7})=-(\sqrt{7}+1)(\sqrt{7}-1)=-(7-1)=-6\\\\x^{2}+2x-6=0$