Question

Составьте квадратные уравнения с корнями

Answer 1

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

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

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

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