Đáp án + Giải thích các bước giải:
`a) x(x - 1) - (x + 1)(x - 2) = 2` $\\$ `<=> x^2 - x - (x^2 - 2x + x - 2) = 2` $\\$ `<=> x^2 - x - x^2 + 2x - x + 2 = 2` $\\$ `<=> 0x = 0`
Phương trình có vô số nghiệm
=> `S=RR`
`b) (3x - 2)(x^2 + 1) = (3x-2)` $\\$ `<=> (3x - 2)(x^2 + 1) - (3x - 2) = 0` $\\$ `<=> (3x - 2)(x^2 + 1 - 1) = 0` $\\$ `<=> (3x - 2)*x^2 = 0 <=> `\(\left[ \begin{array}{l}3x - 2 = 0\\x^2 = 0\end{array} \right.\) $\\$ `<=> `\(\left[ \begin{array}{l}x=\frac{2}{3}\\x=0\end{array} \right.\)
Vậy `S = {2/3;0}`
`c) 2/x - 1/[x(x - 3)] = 1/(3x - 4)(x ne0,x ne3,x ne4/3)` $\\$ `<=> [2(x - 3)]/[x(x - 3)] - 1/[x(x - 3)] = 1/(3x - 4)` $\\$ `<=> [2(x - 3) - 1]/[x(x - 3)] = 1/(3x - 4)` $\\$ `<=> (2x - 6 - 1)/[x(x - 3)] = 1/(3x - 4)` $\\$ `<=> (2x - 7)/[x(x - 3)] = 1/(3x - 4)` $\\$ `<=>(2x - 7)(3x - 4) = x(x - 3)` $\\$ `<=> 6x^2 - 8x - 21x + 28 = x^2 - 3x` $\\$ `<=> 6x^2 - 8x - 21x + 28 - x^2 + 3x = 0` $\\$ `<=> 5x^2 - 26x + 28 = 0`
` <=> 5(x^2 - 26/5x+28/5) = 0` $\\$ `<=> 5[x^2 - 2*x*13/5 + (13/5)^2]-29/5 = 0 <=> 5(x-13/5)^2 - 29/5 = 0` $\\$ `<=> 5(x - 13/5)^2 = 29/5 <=> (x - 13/5)^2 = 29/25` $\\$ `<=> (x - 13/5)^2 - (sqrt{29}/5)^2 = 0`
Tới đây tìm nghiệm nhé
`d) (108 - x)/92 + (107-x)/93 + (106-x)/94 + (105-x)/95 + 4 = 0` $\\$ `<=> ((108-x)/92 + 1)+((107-x)/93+1)+((106-x)/94+1)+((105-x)/95+1) = 0` $\\$ `<=>(200 - x)/92 + (200 - x)/93 + (200 - x)/94 + (200 - x)/95 = 0`$\\$ `<=> (200 - x)(1/92 + 1/93 + 1/94 + 1/95)=0` $\\$ `<=> 200 - x = 0(vì1/92 + 1/93 + 1/94 + 1/95 > 0) <=> x = 200`
Vậy `S = {200}`
