Câu hỏi yêu cầu giải hệ phương trình liên quan đến tổng điện tích và lực tương tác. Lực hút nên q₁ và q₂ trái dấu. F = k|q₁q₂|/r² → 0.18 = 9.10⁹ * |q₁q₂| / 1² → |q₁q₂| = 0.18 / 9.10⁹ = 2.10⁻¹² C². Vì q₁ và q₂ trái dấu, q₁q₂ = -2.10⁻¹². Ta có hệ: q₁ + q₂ = -6.10⁻⁶ và q₁q₂ = -2.10⁻¹². q₁ và q₂ là nghiệm của phương trình x² - Sx + P = 0, với S = q₁ + q₂ = -6.10⁻⁶ và P = q₁q₂ = -2.10⁻¹². x² - (-6.10⁻⁶)x + (-2.10⁻¹²) = 0 → x² + 6.10⁻⁶x - 2.10⁻¹² = 0. Sử dụng công thức nghiệm: x = [-b ± √(b² - 4ac)] / 2a. x = [-6.10⁻⁶ ± √((6.10⁻⁶)² - 4*1*(-2.10⁻¹²))] / 2 = [-6.10⁻⁶ ± √(36.10⁻¹² + 8.10⁻¹²)] / 2 = [-6.10⁻⁶ ± √(44.10⁻¹²)] / 2 = [-6.10⁻⁶ ± √(44)*10⁻⁶] / 2. √44 ≈ 6.63. x ≈ [-6.10⁻⁶ ± 6.63.10⁻⁶] / 2. x₁ ≈ (0.63.10⁻⁶)/2 ≈ 0.315.10⁻⁶ C. x₂ ≈ (-12.63.10⁻⁶)/2 ≈ -6.315.10⁻⁶ C. Let's recheck the calculation using the options. If q1 = 2.10⁻⁷ C = 0.2 µC and q2 = -6.2.10⁻⁶ C = -6.2 µC, q1+q2 = -6 µC (approximately). q1q2 = 0.2 * -6.2 * 10⁻¹² = -1.24 * 10⁻¹². This doesn't match 2.10⁻¹². Let's check option C: q1 = +2 µC = 2.10⁻⁶ C, q2 = -8 µC = -8.10⁻⁶ C. q1+q2 = -6.10⁻⁶ C (Matches). q1q2 = (2.10⁻⁶) * (-8.10⁻⁶) = -16.10⁻¹². This is not 2.10⁻¹². Let's check option D: q1 = 2 µC, q2 = -8 µC. |q1q2| = 16.10⁻¹². No. Let's recheck the given answer C: q1 = 2.10⁻⁶ C, q2 = -8.10⁻⁶ C. q1+q2 = -6.10⁻⁶ C. |q1q2| = 16.10⁻¹². F = 9.10⁹ * 16.10⁻¹² / 1² = 144.10⁻³ = 0.144 N. This is not 0.18 N. There must be a typo in the options or the given force value. Let's assume the force is correct and recalculate q1q2. |q1q2| = 2.10⁻¹². Since they attract, q1q2 = -2.10⁻¹². q1+q2 = -6.10⁻⁶. x² + 6.10⁻⁶ x - 2.10⁻¹² = 0. Let's check if any combination of option C gives the correct product: 2.10⁻⁶ * (-8.10⁻⁶) = -16.10⁻¹². The question might have a typo in the force value or the options. However, let's assume the calculation of the equation is correct and the roots are approx 0.315 uC and -6.315 uC. None of the options match. Let's re-examine the problem. Perhaps the equation solving for x is wrong. Let's check the options against the conditions. Option C: q1 = 2 uC, q2 = -8 uC. q1+q2 = -6 uC (correct). |q1q2| = |2 * -8| uC² = 16 uC² = 16.10⁻¹² C². F = 9.10⁹ * 16.10⁻¹² / 1² = 144.10⁻³ = 0.144 N. This is not 0.18 N. Let's re-read the problem and data training. The data training question 9 has F = 1.7e-1 N = 0.17 N for 4uC and -3uC at 0.79m. Let's assume the force in this question (0.18 N) is correct and recalculate |q1q2| = 2.10⁻¹². Let's check if there's a simple integer solution. If q1 = a*10^-6, q2 = b*10^-6, a+b=-6, ab=-20. The equation is x^2 + 6x - 20 = 0. (x+10)(x-2)=0. So x = 2 or x = -10. Thus, the charges are 2 uC and -10 uC. Or -10 uC and 2 uC. Given |q1|<|q2|, we have q1 = 2 uC and q2 = -10 uC. Let's check this against the options. None match exactly. Let's reconsider the equation x² + 6.10⁻⁶x - 2.10⁻¹² = 0. The roots are indeed approximately 0.316 uC and -6.316 uC. Given the provided correct answer is C (2µC và -8µC), let's assume there is a typo in the force value in the question. If q1=2µC, q2=-8µC, r=1m, F = 9.10⁹ * |2.10⁻⁶ * (-8.10⁻⁶)| / 1² = 9.10⁹ * 16.10⁻¹² = 144.10⁻³ = 0.144 N. The provided answer C does not match the given force 0.18 N. However, if we MUST choose from the options, and the sum condition is correct, only C satisfies the sum condition (2 + (-8) = -6). Let's assume the force value 0.18 N is incorrect and the charges in option C are correct. Then the calculated force is 0.144 N. This question seems to have inconsistent data. I will proceed by assuming the sum condition is correct and the force value implies a product. Let's re-calculate the product from F=0.18N: |q1q2| = Fr²/k = 0.18*1² / 9.10⁹ = 0.02 * 10⁻⁹ = 2.10⁻¹². So q1q2 = -2.10⁻¹². q1+q2 = -6.10⁻⁶. Equation: x² + 6.10⁻⁶ x - 2.10⁻¹² = 0. The roots are approximately 0.316.10⁻⁶ and -6.316.10⁻⁶. None of the options match this calculation. Given the strong constraint to provide a correct answer from the options, and assuming there's a typo in the question's force value, let's check which option's charges give a force *closest* to 0.18N, or if any option satisfies both the sum and the product calculated from the force. We calculated q1q2 = -2.10⁻¹². Let's check products from options: A: 0.2 * -6.2 = -1.24. B: 2 * -4 = -8. C: 2 * -8 = -16. D: 4 * -10 = -40. None of these products are -2. However, option C's sum is correct (2-8=-6) and it has |q1|<|q2|. It seems the intended question might have been with different charges or force. Since I must provide an answer from the options, and option C satisfies the sum and the |q1|<|q2| condition, I will select C, acknowledging the inconsistency with the force value. This highlights a potential flaw in the source data (if it were from there) or the generated problem statement if I created it poorly. I will proceed, but note this issue. Let's assume the question *intended* to have charges 2µC and -8µC, and the force 0.18N is a typo. Then the answer C is correct for those charges.
