Question

gpt:  \(\frac{1}{x^2-3x+3}+\frac{2}{x^2-3x+4}=\frac{6}{x^2-3x+5}\)

Answer 1

Đặt x²-3x+4=a

=>\(\frac{1}{a-1}+\frac{2}{a}=\frac{6}{a+1}\)

ĐKXĐ:a khác 1 ; -1 ;0

=>a²+a+2a²-2=6a²-6a

<=>6a²-3a²-a-6a+2=0

<=>3a²-7a+2=0

<=>(3a-1)(a-2)=0

<=>a=1/3 hoặc a=2

*)a=1/3

=>x²-3x+4=1/3

<=>x²-3x+11/3=0

<=>(x-1,5)²+17/12=0(vô lí)

*)a=2

=>x²-3x+4=2

<=>x²-3x+2=0

<=>(x-1)(x-2)=0

<=>x=1 hoặc x=2

Vậy x={1;2}