Question

складіть квадратне рівняння корені якого =3-√2і 3+√2 ​

Answer 1

$\displaystyle\bf\\x_{1} =3-\sqrt{2} \\\\x_{2} =3+\sqrt{2} \\\\Teorema \ Vieta:\\\\x^{2} +px+q=0\\\\x_{1} +x_{2} =-p\\\\x_{1} \cdot x_{2} =q\\\\-p=3-\sqrt{2} +3+\sqrt{2} =6\\\\p=-6\\\\q=(3-\sqrt{2} )\cdot(3+\sqrt{2} )=3^{2} -(\sqrt{2} )^{2} =9-2=7\\\\\\\boxed{\boxed{x^{2} -6x+7=0}}$