Question

решите уравнения через дискриминант

Answer 1

$1); ; x^2+2(1+sqrt8)x+8sqrt2=0\\frac{D}{4}=(frac{b}{2})^2-ac=(1+sqrt8)^2-2sqrt8= 9+2sqrt8-8sqrt2=9\\x_{1,2}=frac{-frac{b}{2}pm sqrt{frac{D}{4}}}{a}=-(1+sqrt8)pm 3\\x_1=-4-sqrt8=-4-2sqrt2=-2(2+sqrt2); ,\\x_2=2-sqrt8=2-2sqrt2=2(1-sqrt2)\\2); ; x^2+4x-sqrt3+1=0\\frac{D}{4}=2^2-(1-sqrt3)=3+sqrt3\\x_{1,2}=-2pm sqrt{3+sqrt3}\\x_1=-2-sqrt{3+sqrt3}\\x_2=-2+sqrt{3+sqrt3}$

$3); ; frac{(x-1)^2}{5}-frac{x+4}{6}=frac{2x-2}{3}; |cdot 30\\6(x^2-2x+1)-5(x+4)=10(2x-2)\\6x^2-12x+6-5x-20-20x+20=0\\6x^2-37x+6=0\\D=b^2-4ac=1225=35^2; ,; ; ; x_{1,2}=frac{37pm 35}{12}\\x_1=frac{2}{12}=frac{1}{6}; ; ,; ; x_2=frac{72}{12}=6$