Hướng dẫn trả lời:
57.
a) `x^2 + 3x - 18 = 0.`
`→ x^2 + 6x - 3x - 18 = 0.`
`→ (x^2 + 6x) - (3x + 18) = 0.`
`→ x.(x + 6) - 3.(x + 6) = 0.`
`→ (x - 3).(x + 6) = 0.`
`→ `\(\left[ \begin{array}{l}x - 3 = 0.\\x + 6 = 0.\end{array} \right.\)
`→ `\(\left[ \begin{array}{l}x = 3.\\x = -6.\end{array} \right.\)
Vậy `x = 3` hoặc `x = -6.`
b) `8x^2 + 30x + 7 = 0.`
`→ 8x^2 + 28x + 2x + 7 = 0.`
`→ (8x^2 + 28x) + (2x + 7) = 0.`
`→ 4x.(2x + 7) + 1.(2x + 7) = 0.`
`→ (4x + 1).(2x + 7) = 0.`
`→`\(\left[ \begin{array}{l}4x + 1 = 0.\\2x + 7 = 0.\end{array} \right.\)
`→`\(\left[ \begin{array}{l}4x = -1.\\2x = -7.\end{array} \right.\)
`→`\(\left[ \begin{array}{l}x = \dfrac{-1}{4}.\\x = \dfrac{-7}{2}.\end{array} \right.\)
Vậy `x = -1/4` hoặc `x = -7/2.`
c) `x^3 - 11x^2 + 30x = 0.`
`→ x.(x^2 - 11x + 30) = 0.`
`→ x.(x^2 - 5x - 6x + 30) = 0.`
`→ x.[(x^2 - 5x) - (6x - 30)] = 0.`
`→ x.[x.(x - 5) - 6.(x - 5)] = 0.`
`→ x.(x - 6).(x - 5) = 0.`
`→`\(\left[\begin{array}{l}x = 0.\\x - 6 = 0.\\x - 5 = 0.\end{array} \right.\)
`→`\(\left[\begin{array}{l}x = 0.\\x = 6.\\x = 5.\end{array} \right.\)
Vậy `x = 0` hoặc `x = 6` hoặc `x = 5`.
Đáp án:
57
a) `x = 3` hoặc `x = -6.`
b) `x = -1/4` hoặc `x = -7/2.`
c) `x = 0` hoặc `x = 6` hoặc `x = 5`.
