Question

(x-3)^2 + 2(x+1)^2 = 3(4x+1) apartine lui R

Answer 1

$\displaystyle (x-3)^2+2(x+1)^2=3(4x+1) \\ x^2-2 \cdot x \cdot 3+3^2+2(x^2+2 \cdot x \cdot 1+1^2)=12x+3 \\ x^2-6x+9+2(x^2+2x+1)=12x+3 \\ x^2-6x+9+2x^2+4x+2=12x+3 \\ x^2-6x+2x^2+4x-12x=3-9-2 \\ 3x^2-14x=-8 \\ 3x^2-14x+8=0 \\ a=3,b=-14,c=8 \\ \Delta=b^2-4ac=14^2-4 \cdot 3 \cdot 8=196-96=100\ \textgreater \ 0 \\ x_1= \frac{14+ \sqrt{100} }{2 \cdot 3} = \frac{14+10}{6} = \frac{24}{6} =4 \\ \\ x_2= \frac{14- \sqrt{100} }{2 \cdot 3} = \frac{14-10}{6} = \frac{4}{6} = \frac{2}{3} \\ \\ S=\{ \frac{2}{3} ;4 \}$