Hướng dẫn trả lời:
Câu 1:
a) `|-7| + |6| = 7 + 6 = 13`
b) `(-2)^2 - 3^2 - (-2)^3 `
`= 4 - 9 - (-8) `
`= 4 - 9 + 8 `
`= 3`
c) `(1/2)^3 - (1/37)^4cdot(-37/2)^4`
`= (1/2)^3 - [1/37cdot(-37/2)]^4`
`= (1/2)^3 - (-1/2)^4`
`= 1/8 - 1/16`
`= 2/16 - 1/16`
`= 1/16`
Câu 2:
a) `|x| = 6`
`→ x = ± 6`
Vậy `x = ± 6`
b) `|x + 2| = 3`
`→ x + 2 = 3` hoặc `x + 2 = -3`
- Trường hợp 1: `x + 2 = 3`
`→ x = 3 - 2`
`→ x = 1`
- Trường hợp 2: `x + 2 = -3`
`→ x = -3 - 2`
`→ x = -5`
Vậy `x = 1` hoặc `x = -5`
c) `|1/2x - 2| - 1/2 = 1`
`→ |1/2x - 2| = 1 + 1/2`
`→ |1/2x - 2| = 2/2 + 1/2`
`→ |1/2x - 2| = 3/2`
`→ 1/2x - 2 = 3/2` hoặc `1/2x - 2 = -3/2`
- Trường hợp 1: `1/2x - 2 = 3/2`
`→ 1/2x = 3/2 + 2`
`→ 1/2x = 3/2 + 4/2`
`→ 1/2x = 7/2`
`→ x = 7/2 ÷ 1/2`
`→ x = 7/2cdot2/1`
`→ x = 7`
- Trường hợp 2: `1/2x - 2 = -3/2`
`→ 1/2x = -3/2 + 2`
`→ 1/2x = -3/2 + 4/2`
`→ 1/2x = 1/2`
`→ x = 1/2 ÷ 1/2`
`→ x = 1`
Vậy `x = 7` hoặc `x = 1`
d) `(2x + 1)^2 = 2`
`→ (2x + 1)^2 = (sqrt2)^2 = (-sqrt2)^2`
`→ 2x + 1 = sqrt2` hoặc `2x + 1 = -sqrt2`
- Trường hợp 1: `2x + 1 = sqrt2`
`→ 2x = sqrt2 - 1`
`→ x = {sqrt2 - 1}/2`
- Trường hợp 2:
`2x + 1 = -sqrt2`
`→ 2x = -sqrt2 - 1`
`→ x = {-sqrt2 - 1}/2`
Vậy `x = {sqrt2 - 1}/2` hoặc `x = {-sqrt2 - 1}/2`
