Giải phương trình sau :
a) x(x-1)-(x+1)(x-2)=2
b) (3x-2)(x^2+1)=3x-2
c) 2/x – 1/x(x-3) = 1/3x-4
d) 108-x/92 + 107-x/93 +106-x/94 + 105-x/95 + 4 = 0
Giải phương trình sau :
a) x(x-1)-(x+1)(x-2)=2
b) (3x-2)(x^2+1)=3x-2
c) 2/x – 1/x(x-3) = 1/3x-4
d) 108-x/92 + 107-x/93 +106-x/94 + 105-x/95 + 4 = 0
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}`