Tìm x biết a) ( 3x + 1 ) ( 3x – 1 ) – ( x – 2 ) ( x^2 + 2x + 4 ) = x (6 – x^3) b) 5x ( x – 3 )^2 + 5 ( x – 4 ) ( x + 4 ) – 5x^3 = -5x ( 6x – 1 ) c)

Đáp án:

 

Giải thích các bước giải:

 a) (3x -1).(3x +1) -(x -2).(x² +2x +4) =x.(6 -x²)

⇔9x² -1 -x³ +8 =6x -x³

⇔9x² -6x +7 =0

⇔(9x² -6x +1) +6 =0

⇔(3x -1)² =-6 (vô lí)

PT vô nghiệm

b)5x.(x-3)² +5.(x-4).(x +4) -5x³ =-5x.(6x -1)

⇔5x.(x² -6x +9) +5.(x² -16) -5x³ =-30x² +5x

⇔5x³ -30x² +45x  +5x² -80 -5x³ +30x² -5x =0

⇔5x² +40x -80 =0

⇔5.(x² +8x -16) =0

⇔x² +8x  =16

⇔x² +8x +16 =32

⇔(x +4)² =32

⇔x +4 =±$\sqrt[]{32}$

⇔ x =±$\sqrt[]{32}$ -4

c) x².(3x+1) -(x -3)² =-9

⇔3x³ +x² -x² +6x -9 =-9

⇔3x³ +6x =0

⇔x³ +2x=0

⇔x.(x² +2) =0

⇔x =0  (vì x² +2 >0)

d)(2x +5).(4x² -10x +25) -(2x +1)² =52

⇔8x³ +125 -4x² -4x -1 =52

⇔8x³ -4x² -4x  +72 =0

⇔8x³ +16x² -20x² -40x +36x +72 =0

⇔(8x³ +16x²) -( 20x² +40x )+(36x +72) =0

⇔8x².(x +2) -20x.(x +2) +36.(x +2) =0

⇔(x +2).( 8x² -20x +36) =0

⇔x+2 =0 (vì 8x² -20x +36 >0)

⇔x =-2

Trả lời