Đáp án + Giải thích các bước giải:
Câu `1`:
a, `(4x - 1/3)^2 + 26/25 = 3`
` (4x - 1/3)^2 = 3 - 26/25`
` (4x - 1/3)^2 = 75/25 - 26/25`
` (4x - 1/3)^2 = 49/25`
` (4x - 1/3)^2 = (7/5)^2 = (-7/5)^2`
`=> 4x - 1/3 = 7/5` hoặc `4x - 1/3 = -7/5`
Nếu `4x - 1/3 = 7/5` ; Nếu `4x - 1/3 = -7/5`
` 4x = 7/5 + 1/3` ; ` 4x = (-7)/5 + 1/3`
` 4x = 21/15 + 5/15` ; ` 4x = (-21)/15 + 5/15`
` 4x = 26/15` ; ` 4x = -16/15`
` x = 26/15 : 4` ; `x = -16/15 : 4`
` x = 13/30` ; ` x = -4/15`
Vậy `x \in {13/30 ; -4/15}`
b, `(2 - x/5)^3 - 20/9 = 4/27`
` (2 - x/5)^3 = 4/27 + 20/9`
` (2 - x/5)^3 = 4/27 + 60/27`
` (2 - x/5)^3 = 64/27`
` (2 - x/5)^3 = (4/3)^3`
`=> 2 - x/5 = 4/3`
` x/5 = 2 - 4/3`
` x/5 = 6/3 - 4/3`
` x/5 = 2/3`
` x = (5 . 2)/3`
` x = 10/3`
Vậy `x = 10/3`
c, `| 3x + 1/3| - 1/2 = 4`
` |3x + 1/3| = 4 + 1/2`
` |3x + 1/3| = 8/2 + 1/2`
` |3x + 1/3| = 9/2`
`=> 3x + 1/3 = 9/2` hoặc `3x + 1/3 = -9/2`
Nếu `3x + 1/3 = 9/2` ; Nếu `3x + 1/3 = -9/2`
` 3x = 9/2 - 1/3` ; `3x = -9/2 - 1/3`
` 3x = 27/6 - 2/6` ; `3x = -27/6 - 2/6`
` 3x = 25/6` ; `3x = -29/6`
` x = 25/6 : 3` ; `x = -29/6 : 3`
` x = 25/18` ; `x = -29/18`
Vậy `x \in {25/18 ; -29/18}`
