giải các pt sau : a) 7x+21=0 b)x+5/4-2x-3/3=6x-1/8+2x-1/12 c)x+1/65+x+3/63=x+5/61+x+7/59 08/07/2021 Bởi Parker giải các pt sau : a) 7x+21=0 b)x+5/4-2x-3/3=6x-1/8+2x-1/12 c)x+1/65+x+3/63=x+5/61+x+7/59
$a)$ `7x+21=0` `⇔ 7x = -21` `⇔ x = -3` Vậy `S= {-3}` $b)$ `(x+5)/4 – (2x-3)/3= (6x-1)/8 + (2x-1)/12` `⇔ [3.(x+5)]/12 – (4.(2x-3))/12 = (3.(6x-1))/24 + [2.(2x-1)]/24` `⇔ (3x +15)/12 – (8x -12)/12 = (18x -3)/24 + (4x -2)/24` `⇔ (3x +15 -8x +12)/12 = (18x -3 +4x -2)/24` `⇔ (-5x +27)/12 = (22x -5)/24` `⇒ 24.(-5x +27) = 12.(22x -5)` `⇔ -120x +648 = 264x – 60` `⇔ -120x -264x = -60 -648` `⇔ -384x = -708` `⇔ x = 59/32` Vậy` S = {59/32}` $c)$ `(x+1)/65 + (x+3)/63= (x+5)/61 + (x+7)/59` `⇔ (x+1)/65 +1 +(x+3)/63 +1 = 1+ (x+5)/61 +1 +(x+7)/59` `⇔ (x +66)/65 + (x +66)/63 = (x +66)/61 + (x +66)/59` `⇔ (x +66)/65 + (x +66)/63 – (x +66)/61 – (x +66)/59 = 0` `⇔ (x +66).( 1/65 + 1/63 – 1/61 – 1/59)^{(1)} = 0` `[`Vì `(1) ne 0]` `⇒ x +66 = 0` `⇒ x = -66` Vậy `S = {-66}` Bình luận
$a)$ `7x+21=0`
`⇔ 7x = -21`
`⇔ x = -3`
Vậy `S= {-3}`
$b)$ `(x+5)/4 – (2x-3)/3= (6x-1)/8 + (2x-1)/12`
`⇔ [3.(x+5)]/12 – (4.(2x-3))/12 = (3.(6x-1))/24 + [2.(2x-1)]/24`
`⇔ (3x +15)/12 – (8x -12)/12 = (18x -3)/24 + (4x -2)/24`
`⇔ (3x +15 -8x +12)/12 = (18x -3 +4x -2)/24`
`⇔ (-5x +27)/12 = (22x -5)/24`
`⇒ 24.(-5x +27) = 12.(22x -5)`
`⇔ -120x +648 = 264x – 60`
`⇔ -120x -264x = -60 -648`
`⇔ -384x = -708`
`⇔ x = 59/32`
Vậy` S = {59/32}`
$c)$ `(x+1)/65 + (x+3)/63= (x+5)/61 + (x+7)/59`
`⇔ (x+1)/65 +1 +(x+3)/63 +1 = 1+ (x+5)/61 +1 +(x+7)/59`
`⇔ (x +66)/65 + (x +66)/63 = (x +66)/61 + (x +66)/59`
`⇔ (x +66)/65 + (x +66)/63 – (x +66)/61 – (x +66)/59 = 0`
`⇔ (x +66).( 1/65 + 1/63 – 1/61 – 1/59)^{(1)} = 0` `[`Vì `(1) ne 0]`
`⇒ x +66 = 0`
`⇒ x = -66`
Vậy `S = {-66}`