X1*X2=-16 X1+X2=11,25 X1=? X2=?

To solve the system of equations: 1. \( X_1 \times X_2 = -16 \) (Equation 1) 2. \( X_1 + X_2 = 11.25 \) (Equation 2) We can express \( X_2 \) in terms of \( X_1 \) using Equation 2: \[ X_2 = 11.25 - X_1 \] Now, we can substitute this expression for \( X_2 \) into Equation 1: \[ X_1 \times (11.25 - X_1) = -16 \] Expanding this gives: \[ 11.25X_1 - X_1^2 = -16 \] Rearranging the equation leads to: \[ X_1^2 - 11.25X_1 - 16 = 0 \] Now we can solve this quadratic equation using the quadratic formula: \[ X_1 = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \] In this case, \( a = 1 \), \( b = -11.25 \), and \( c = -16 \): \[ X_1 = \frac{-(-11.25) \pm \sqrt{(-11.25)^2 - 4(1)(-16)}}{2(1)} \] Calculating the discriminant: \[ (-11.25)^2 = 126.5625 \] \[ 4 \times 1 \times -16 = -64 \] So: \[ b^2 - 4ac = 126.5625 + 64 = 190.5625 \] Now substituting back in: \[ X_1 = \frac{11.25 \pm \sqrt{190.5625}}{2} \] Calculating the square root: \[ \sqrt{190.5625} \approx 13.8 \] Now substituting back: \[ X_1 = \frac{11.25 \pm 13.8}{2} \] We have two options for \( X_1 \): 1. \( X_1 = \frac{11.25 + 13.8}{2} \approx \frac{25.05}{2} \approx 12.525 \) 2. \( X_1 = \frac{11.25 - 13.8}{2} \approx \frac{-2.55}{2} \approx -1.275 \) Now, we calculate \( X_2 \) for each \( X_1 \): 1. For \( X_1 \approx 12.525 \): \[ X_2 = 11.25 - 12.525 \approx -1.275 \] 2. For \( X_1 \approx -1.275 \): \[ X_2 = 11.25 - (-1.275) \approx 12.525 \] Thus, the pairs \((X_1, X_2)\) are: - \( X_1 \approx 12.525 \) and \( X_2 \approx -1.275 \) - \( X_1 \approx -1.275 \) and \( X_2 \approx 12.525 \) Final answers: - \( X_1 \approx 12.525, X_2 \approx -1.275 \) - or - \( X_1 \approx -1.275, X_2 \approx 12.525 \)