発展問題 問題
上級練習のためのより難しい二次方程式と代数の課題。
難易度が混ざったものではなく、利用可能な最も難しい数学の問題を求める人のために、より簡単な練習セットから取り出された難しい数学の問題と答え付きの難しい数学の問題のコレクションです。
はじめる： 発展問題
発展問題の例題
以下の例題は現在、英語のみで提供されています。
1. Solve: 3x^2 + 3x - 60 = 0+
答え: x = -5 or x = 4
Step 1: Identify a = 3, b = 3, c = -60. Step 2: Compute the discriminant: b^2 - 4ac = 3^2 - 4(3)(-60) = 729. Step 3: Apply the quadratic formula: x = (-b ± √discriminant) / 2a = (-3 ± 27) / 6. Step 4: x = -5 or x = 4.
2. Solve: 5x^2 + 10x - 15 = 0+
答え: x = -3 or x = 1
Step 1: Identify a = 5, b = 10, c = -15. Step 2: Compute the discriminant: b^2 - 4ac = 10^2 - 4(5)(-15) = 400. Step 3: Apply the quadratic formula: x = (-b ± √discriminant) / 2a = (-10 ± 20) / 10. Step 4: x = -3 or x = 1.
3. Solve: 6x^2 - 96 = 0+
答え: x = 4 or x = -4
Step 1: Identify a = 6, b = 0, c = -96. Step 2: Compute the discriminant: b^2 - 4ac = 0^2 - 4(6)(-96) = 2304. Step 3: Apply the quadratic formula: x = (-b ± √discriminant) / 2a = (0 ± 48) / 12. Step 4: x = 4 or x = -4.
4. Solve: 3x^2 + 21x + 36 = 0+
答え: x = -3 or x = -4
Step 1: Identify a = 3, b = 21, c = 36. Step 2: Compute the discriminant: b^2 - 4ac = 21^2 - 4(3)(36) = 9. Step 3: Apply the quadratic formula: x = (-b ± √discriminant) / 2a = (-21 ± 3) / 6. Step 4: x = -3 or x = -4.
5. Solve: 9x^2 + 72x + 144 = 0+
答え: x = -4
Step 1: Identify a = 9, b = 72, c = 144. Step 2: Compute the discriminant: b^2 - 4ac = 72^2 - 4(9)(144) = 0. Step 3: Apply the quadratic formula: x = (-b ± √discriminant) / 2a = (-72 ± 0) / 18. Step 4: x = -4.
6. Solve: 2x^2 - 14x + 24 = 0+
答え: x = 4 or x = 3
Step 1: Identify a = 2, b = -14, c = 24. Step 2: Compute the discriminant: b^2 - 4ac = (-14)^2 - 4(2)(24) = 4. Step 3: Apply the quadratic formula: x = (-b ± √discriminant) / 2a = (14 ± 2) / 4. Step 4: x = 4 or x = 3.