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4 ESO Academics - Unit 04 - Exercises 4.4.2 - Other Types of Equations
- 1. UNIT 04 January 1. Write an equation with this solutions: a) 𝟎𝟎; 𝟏𝟏; 𝟐𝟐 𝒂𝒂𝒏𝒏𝒏𝒏 𝟑𝟑 b) ±√𝟐𝟐; ±√𝟑𝟑 c) 𝟐𝟐; −𝟐𝟐; 𝟒𝟒 𝒂𝒂𝒏𝒏𝒏𝒏 𝟓𝟓 d) 𝑫𝑫𝒐𝒐𝒐𝒐𝒐𝒐𝒐𝒐𝒐𝒐𝒐𝒐 𝟎𝟎 𝒂𝒂𝒏𝒏𝒏𝒏 𝟏𝟏 2. Which kind of equations have we? 𝒂𝒂) (𝒙𝒙𝟐𝟐 − 𝟒𝟒)(𝒙𝒙 + 𝟓𝟓)𝒙𝒙 = 𝟎𝟎 𝒃𝒃) 𝒙𝒙 − √𝒙𝒙 − 𝟏𝟏 = √𝟒𝟒𝟒𝟒 + 𝟗𝟗 𝐜𝐜) 𝒙𝒙𝟐𝟐 𝒙𝒙 + 𝟑𝟑 − 𝒙𝒙 = 𝟐𝟐 𝒅𝒅) 𝒙𝒙𝟐𝟐 − 𝒙𝒙𝟒𝟒 = 𝒙𝒙𝟒𝟒 + 𝟓𝟓𝒙𝒙𝟐𝟐 Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.4.2.1
- 2. UNIT 04 January 3. Solve: a) 𝒙𝒙𝟒𝟒 − 𝟐𝟐𝟐𝟐𝒙𝒙𝟐𝟐 + 𝟔𝟔𝟔𝟔 = 𝟎𝟎 b) 𝒙𝒙𝟒𝟒 − 𝟐𝟐𝟐𝟐𝒙𝒙𝟐𝟐 + 𝟐𝟐𝟐𝟐 = 𝟎𝟎 c) 𝒙𝒙𝟒𝟒 − 𝟒𝟒𝟒𝟒𝒙𝒙𝟐𝟐 + 𝟏𝟏𝟏𝟏𝟏𝟏 = 𝟎𝟎 d) 𝒙𝒙𝟐𝟐(𝒙𝒙𝟐𝟐 − 𝟑𝟑𝟑𝟑) − 𝒙𝒙𝟐𝟐 = −𝟑𝟑𝟑𝟑 e) 𝟏𝟏𝟑𝟑𝒙𝒙𝟐𝟐 − 𝒙𝒙𝟒𝟒 = 𝟑𝟑𝟑𝟑 f) (𝒙𝒙𝟐𝟐 − 𝟐𝟐𝟓𝟓)𝒙𝒙𝟐𝟐 = (𝒙𝒙𝟐𝟐 − 𝟐𝟐𝟐𝟐) ∙ 𝟗𝟗 Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.4.2.2
- 3. UNIT 04 January g) 𝒙𝒙𝟒𝟒 − 𝟏𝟏 = 𝟎𝟎 h) 𝒙𝒙𝟒𝟒 − 𝟐𝟐𝟐𝟐𝒙𝒙𝟐𝟐 = 𝟏𝟏𝟏𝟏𝟏𝟏 i) 𝒙𝒙𝟒𝟒 + 𝟑𝟑𝒙𝒙𝟐𝟐 + 𝟐𝟐 = 𝟎𝟎 j) 𝒙𝒙𝟒𝟒 − 𝟏𝟏𝟓𝟓𝒙𝒙𝟐𝟐 = −𝟓𝟓𝟓𝟓 k) 𝒙𝒙𝟒𝟒 + 𝟏𝟏𝟏𝟏𝒙𝒙𝟐𝟐 + 𝟕𝟕𝟎𝟎 = 𝟎𝟎 l) 𝒙𝒙𝟒𝟒 + 𝟏𝟏𝟏𝟏 = 𝟗𝟗𝒙𝒙𝟐𝟐 Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.4.2.3
- 4. UNIT 04 January 4. Solve: a) 𝒙𝒙𝟑𝟑 − 𝟕𝟕𝒙𝒙𝟐𝟐 − 𝟒𝟒𝟒𝟒 + 𝟐𝟐𝟐𝟐 = 𝟎𝟎 b) 𝒙𝒙𝟑𝟑 + 𝟕𝟕𝟕𝟕 + 𝟏𝟏𝟏𝟏 = 𝟕𝟕𝒙𝒙𝟐𝟐 c) 𝒙𝒙𝟑𝟑 + 𝟏𝟏𝟏𝟏𝒙𝒙𝟐𝟐 = 𝟒𝟒𝟒𝟒 + 𝟒𝟒𝟒𝟒 d) 𝒙𝒙𝟑𝟑 + 𝟑𝟑𝒙𝒙𝟐𝟐 = 𝟏𝟏𝟏𝟏𝟏𝟏 + 𝟒𝟒𝟒𝟒 e) 𝒙𝒙𝟑𝟑 − 𝟐𝟐𝒙𝒙𝟐𝟐 + 𝟐𝟐𝟐𝟐 = 𝟏𝟏𝟏𝟏𝟏𝟏 f) 𝟒𝟒𝒙𝒙𝟑𝟑 + 𝒙𝒙𝟐𝟐 − 𝟒𝟒𝟒𝟒 − 𝟏𝟏 = 𝟎𝟎 Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.4.2.4
- 5. UNIT 04 January g) 𝟐𝟐𝒙𝒙𝟑𝟑 − 𝟓𝟓𝒙𝒙𝟐𝟐 − 𝟐𝟐𝟐𝟐𝟐𝟐 − 𝟏𝟏𝟏𝟏 = 𝟎𝟎 h) 𝟏𝟏𝟎𝟎𝒙𝒙𝟑𝟑 + 𝟐𝟐𝟐𝟐𝒙𝒙𝟐𝟐 − 𝟑𝟑𝟑𝟑𝟑𝟑 − 𝟕𝟕 = 𝟎𝟎 i) 𝒙𝒙𝟑𝟑 − 𝟑𝟑𝒙𝒙𝟐𝟐 − 𝟑𝟑𝟑𝟑𝟑𝟑 − 𝟑𝟑𝟑𝟑 = 𝟎𝟎 j) 𝒙𝒙𝟑𝟑 = 𝒙𝒙𝟐𝟐 + 𝟐𝟐𝟐𝟐𝟐𝟐 + 𝟑𝟑𝟑𝟑 k) 𝒙𝒙𝟑𝟑 + 𝟔𝟔𝒙𝒙𝟐𝟐 = 𝟐𝟐𝟐𝟐𝟐𝟐 + 𝟏𝟏𝟏𝟏𝟏𝟏 l) 𝒙𝒙𝟑𝟑 − 𝟏𝟏𝟏𝟏𝒙𝒙𝟐𝟐 + 𝟓𝟓𝟓𝟓 + 𝟏𝟏𝟏𝟏𝟏𝟏 = 𝟎𝟎 Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.4.2.5
- 6. UNIT 04 January 5. Solve: 𝒂𝒂) 𝟏𝟏 𝒙𝒙 + 𝟏𝟏 + 𝒙𝒙 𝟒𝟒 − 𝒙𝒙 = 𝟐𝟐 𝒃𝒃) 𝟑𝟑 𝒙𝒙 − 𝒙𝒙 − 𝟏𝟏 𝒙𝒙 + 𝟐𝟐 = 𝒙𝒙 + 𝟐𝟐 𝒙𝒙 𝒄𝒄) 𝟐𝟐 𝒙𝒙 + 𝟑𝟑 + 𝒙𝒙 − 𝟏𝟏 𝒙𝒙𝟐𝟐 = 𝟏𝟏 𝒙𝒙 𝒅𝒅) 𝒙𝒙 𝟏𝟏 − 𝒙𝒙 + 𝟐𝟐 𝒙𝒙𝟐𝟐 − 𝟏𝟏 = 𝒙𝒙 − 𝟖𝟖 𝒙𝒙 + 𝟏𝟏 Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.4.2.6
- 7. UNIT 04 January 𝒆𝒆) 𝟏𝟏 𝒙𝒙 = 𝒙𝒙 − 𝟏𝟏 + 𝒙𝒙 𝟒𝟒 − 𝒙𝒙 𝒇𝒇) 𝒙𝒙𝟐𝟐 + 𝒙𝒙 𝟑𝟑 + 𝟏𝟏 𝒙𝒙 = 𝟏𝟏 𝟔𝟔 𝐠𝐠) 𝟑𝟑 𝒙𝒙 + 𝟏𝟏 − 𝟏𝟏 𝒙𝒙𝟐𝟐 + 𝟐𝟐𝟐𝟐 + 𝟏𝟏 = 𝟐𝟐𝒙𝒙 𝒉𝒉) 𝟐𝟐 𝟑𝟑 + 𝟒𝟒𝟒𝟒 + 𝒙𝒙 𝒙𝒙 + 𝟏𝟏 = 𝒙𝒙 + 𝟑𝟑 Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.4.2.7
- 8. UNIT 04 January 6. Solve: 𝒂𝒂) √𝒙𝒙 + 𝟑𝟑 = 𝒙𝒙 − 𝟑𝟑 𝒃𝒃) 𝟏𝟏𝟎𝟎 − 𝟒𝟒√𝟏𝟏𝟏𝟏 + 𝒙𝒙 = 𝒙𝒙 + 𝟖𝟖 𝒄𝒄) 𝟐𝟐𝟎𝟎 − √𝟓𝟓𝟓𝟓 + 𝟏𝟏 = 𝟓𝟓𝟓𝟓 + 𝟏𝟏 𝒅𝒅) 𝟕𝟕𝒙𝒙 = √𝟕𝟕𝟕𝟕 + 𝟐𝟐 + 𝟓𝟓𝟓𝟓 Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.4.2.8
- 9. UNIT 04 January 𝒆𝒆) 𝒙𝒙 = 𝟐𝟐√𝟒𝟒𝟒𝟒 + 𝟗𝟗 𝒇𝒇) 𝟑𝟑 + √𝟑𝟑𝟑𝟑 + 𝟏𝟏𝟏𝟏 = √𝒙𝒙 − 𝟒𝟒 + 𝟕𝟕 𝐠𝐠) √𝟕𝟕𝒙𝒙 + 𝟏𝟏 − √𝒙𝒙 − 𝟏𝟏 = 𝟒𝟒 𝒉𝒉) 𝟕𝟕 − √𝟐𝟐𝟐𝟐 + 𝟓𝟓 = √𝒙𝒙 − 𝟏𝟏 − 𝟏𝟏 𝒊𝒊) √𝒙𝒙 + 𝟐𝟐 − √𝟏𝟏𝟖𝟖 − 𝒙𝒙 = √𝟏𝟏𝟎𝟎 + 𝟏𝟏𝟏𝟏𝟏𝟏 Axel Cotón Gutiérrez Mathematics 4º ESO Exercises – 4.4.2.9