----- Nội dung dịch tự động từ ảnh ----- Bài 4: Tìm x biết: a, x²-9=0. a, 4x²-4=0.1 a, 4x²-36 0. a, (5x-4)²-49x2=0. a. (3x-5)-(x+1)=0. a, (2x+1)-(x-1)=0. a, (3x-1)-(x+5)=0. a, (2x-3)-(x+5)=0. a, (3x-4)-(x+2)=0. a, x(x+1)-x²+1=0. a, 4x.(x-2)-6+3x=0. a, x(x+2)-3(x+2)=0. a, 8x.(x-5)-2x+10=0. a, x(2x-3)-2(3-2x)=0. b, (x-1)+x(4-x)=11. b, (x-5)-x.(x+2)=5. b, x(x+4)-x-6x=10. b, 2(x+3)-x-3x=0. b, 3x(x-5)-x+25=0. b, 3x (2x-1)-24x+12=0. b, x(x-2019)-x+2019=0. b, 3x (x-2019)-x+2019-0. b, (x+2)-(x-2).(x+2)=0. b, (x+3)-(x+2).(x-2)=4x+17. b. (2x+1)-(4x-1).(x-3)-15=0. b, (2x+3).(x-1)+(2x-3).(1-x)=0. b. 2(5x-8)-3(4x-5)=4(3x-4)+11. b. (3x-1).(2x-7)-(1-3x).(6x-5)=0.
2 trả lời
64 Tham khảo câu trả lời từ Trợ lý ảo Lazi Dưới đây là lời giải cho các phương trình trong bài tập: a) \( x^2 - 9 = 0 \) \[ x^2 = 9 \] \[ x = \pm 3 \] b) \( 4x^2 - 4 = 0 \) \[ 4x^2 = 4 \] \[ x^2 = 1 \] \[ x = \pm 1 \] c) \( 4x^2 - 36 = 0 \) \[ 4x^2 = 36 \] \[ x^2 = 9 \] \[ x = \pm 3 \] d) \( (5x - 4)^2 - 49x^2 = 0 \) \[ 25x^2 - 40x + 16 - 49x^2 = 0 \] \[ -24x^2 - 40x + 16 = 0 \] \[ 24x^2 + 40x - 16 = 0 \] \[ 3x^2 + \frac{5}{3}x - \frac{2}{3} = 0 \] \[ x = -\frac{5}{6} \pm \frac{\sqrt{(5/6)^2 + 4 \cdot 3 \cdot 2/3}}{2 \cdot 3} \] e) \( (3x - 5) - (x + 1) = 0 \) \[ 3x - 5 - x - 1 = 0 \] \[ 2x - 6 = 0 \] \[ x = 3 \] f) \( (2x + 1) - (x - 1) = 0 \) \[ 2x + 1 - x + 1 = 0 \] \[ x + 2 = 0 \] \[ x = -2 \] g) \( (3x - 1) - (x + 5) = 0 \) \[ 3x - 1 - x - 5 = 0 \] \[ 2x - 6 = 0 \] \[ x = 3 \] h) \( (2x - 3) - (x + 5) = 0 \) \[ 2x - 3 - x - 5 = 0 \] \[ x - 8 = 0 \] \[ x = 8 \] i) \( (3x - 4) - (x + 2) = 0 \) \[ 3x - 4 - x - 2 = 0 \] \[ 2x - 6 = 0 \] \[ x = 3 \] j) \( x(x + 1) - x^2 + 1 = 0 \) \[ x^2 + x - x^2 + 1 = 0 \] \[ x + 1 = 0 \] \[ x = -1 \] k) \( 4x(x - 2) - 6 + 3x = 0 \) \[ 4x^2 - 8x - 6 + 3x = 0 \] \[ 4x^2 - 5x - 6 = 0 \] \[ x = \frac{5 \pm \sqrt{25 + 96}}{8} \] \[ x = \frac{5 \pm 11}{8} \] \[ x = 2 \text{ or } x = -\frac{3}{4} \] l) \( x(x + 2) - 3(x + 2) = 0 \) \[ x(x + 2) - 3(x + 2) = 0 \] \[ (x - 3)(x + 2) = 0 \] \[ x = 3 \text{ or } x = -2 \] m) \( 8x(x - 5) - 2x + 10 = 0 \) \[ 8x^2 - 40x - 2x + 10 = 0 \] \[ 8x^2 - 42x + 10 = 0 \] \[ x = \frac{42 \pm \sqrt{1764 - 320}}{16} \] \[ x = \frac{42 \pm \sqrt{1444}}{16} \] \[ x = \frac{42 \pm 38}{16} \] \[ x = 5 \text{ or } x = \frac{1}{4} \] n) \( x(2x - 3) - 2(3 - 2x) = 0 \) \[ 2x^2 - 3x - 6 + 4x = 0 \] \[ 2x^2 + x - 6 = 0 \] \[ x = \frac{-1 \pm \sqrt{1 + 48}}{4} \] \[ x = \frac{-1 \pm 7}{4} \] \[ x = 1.5 \text{ or } x = -2 \] o) \( (x - 1)^2 + x(4 - x) = 11 \) \[ x^2 - 2x + 1 + 4x - x^2 = 11 \] \[ 2x + 1 = 11 \] \[ 2x = 10 \] \[ x = 5 \] p) \( (x - 5)^2 - x(x + 2) = 5 \) \[ x^2 - 10x + 25 - x^2 - 2x = 5 \] \[ -12x + 25 = 5 \] \[ -12x = -20 \] \[ x = \frac{5}{3} \] q) \( x(x + 4) - x - 6x = 10 \) \[ x^2 + 4x - x - 6x = 10 \] \[ x^2 - 3x = 10 \] \[ x^2 - 3x - 10 = 0 \] \[ x = \frac{3 \pm \sqrt{9 + 40}}{2} \] \[ x = \frac{3 \pm 7}{2} \] \[ x = 5 \text{ or } x = -2 \] r) \( 2(x + 3) - x - 3x = 0 \) \[ 2x + 6 - x - 3x = 0 \] \[ -2x + 6 = 0 \] \[ x = 3 \] s) \( 3x(x - 5) - x + 25 = 0 \) \[ 3x^2 - 15x - x + 25 = 0 \] \[ 3x^2 - 16x + 25 = 0 \] \[ x = \frac{16 \pm \sqrt{256 - 300}}{6} \] \[ x = \frac{16 \pm \sqrt{-44}}{6} \] \[ \text{No real solution} \] t) \( 3x(2x - 1) - 24x + 12 = 0 \) \[ 6x^2 - 3x - 24x + 12 = 0 \] \[ 6x^2 - 27x + 12 = 0 \] \[ x = \frac{27 \pm \sqrt{729 - 288}}{12} \] \[ x = \frac{27 \pm \sqrt{441}}{12} \] \[ x = \frac{27 \pm 21}{12} \] \[ x = 4 \text{ or } x = \frac{1}{2} \] u) \( x(x - 2019) - x + 2019 = 0 \) \[ x^2 - 2019x - x + 2019 = 0 \] \[ x^2 - 2020x + 2019 = 0 \] \[ x = \frac{2020 \pm \sqrt{4080400 - 8076}}{2} \] \[ x = \frac{2020 \pm \sqrt{4072324}}{2} \] \[ x = \frac{2020 \pm 2018}{2} \] \[ x = 2019 \text{ or } x = 1 \] v) \( 3x(x - 2019) - x + 2019 = 0 \) \[ 3x^2 - 6057x - x + 2019 = 0 \] \[ 3x^2 - 6058x + 2019 = 0 \] \[ x = \frac{6058 \pm \sqrt{36700864 - 24228}}{6} \] \[ x = \frac{6058 \pm \sqrt{36676636}}{6} \] \[ x = \frac{6058 \pm 6056}{6} \] \[ x = 2019 \text{ or } x = \frac{1}{3} \] w) \( (x + 2) - (x - 2)(x + 2) = 0 \) \[ x + 2 - (x^2 - 4) = 0 \] \[ x + 2 - x^2 + 4 = 0 \] \[ -x^2 + x + 6 = 0 \] \[ x = \frac{-1 \pm \sqrt{1 + 24}}{2} \] \[ x = \frac{-1 \pm 5}{2} \] \[ x = 2 \text{ or } x = -3 \] x) \( (x + 3) - (x + 2)(x - 2) = 4x + 17 \) \[ x + 3 - (x^2 - 4) = 4x + 17 \] \[ x + 3 - x^2 + 4 = 4x + 17 \] \[ -x^2 - 3x - 10 = 0 \] \[ x = \frac{-3 \pm \sqrt{9 + 40}}{2} \] \[ x = \frac{-3 \pm 7}{2} \] \[ x = 2 \text{ or } x = -5 \] y) \( (2x + 1) - (4x - 1)(x - 3) - 15 = 0 \) \[ 2x + 1 - (4x^2 - 13x + 3) - 15 = 0 \] \[ 2x + 1 - 4x^2 + 13x - 3 - 15 = 0 \] \[ -4x^2 + 15x - 17 = 0 \] \[ x = \frac{15 \pm \sqrt{225 + 272}}{8} \] \[ x = \frac{15 \pm 19}{8} \] \[ x = 4.25 \text{ or } x = -0.5 \] z) \( (2x + 3)(x - 1) + (2x - 3)(1 - x) = 0 \) \[ 2x^2 + x - 3 + 2x - 3 = 0 \] \[ 2x^2 + 3x - 6 = 0 \] \[ x = \frac{-3 \pm \sqrt{9 + 48}}{4} \] \[ x = \frac{-3 \pm 7}{4} \] \[ x = 1 \text{ or } x = -2.5 \] aa) \( 2(5x - 8) - 3(4x - 5) = 4(3x - 4) + 11 \) \[ 10x - 16 - 12x + 15 = 12x - 16 + 11 \] \[ -2x - 1 = 12x - 5 \] \[ -2x - 12x = -5 + 1 \] \[ -14x = -4 \] \[ x = \frac{2}{7} \] bb) \( (3x - 1)(2x - 7) - (1 - 3x)(6x - 5) = 0 \) \[ 6x^2 - 21x - 2x + 7 - 6x + 15x = 0 \] \[ 6x^2 - 14x + 7 = 0 \] \[ x = \frac{14 \pm \sqrt{196 - 168}}{12} \] \[ x = \frac{14 \pm 4}{12} \] \[ x = 1.5 \text{ or } x = 0.833 \] Hy vọng các lời giải trên sẽ giúp bạn hiểu rõ hơn về cách giải các phương trình này.