Chapter 10 - Section 10.8 - Systems of Nonlinear Equations - 10.8 Exercises - Page 754: 24

$(4, 6)$ $(-4, -6)$

Given the system of equations: 1. $xy = 24$ 2. $2x^2 - y^2 + 4 = 0$ It asks to find all solutions. Substitute $y = 24/x$ $2x^2 - (24/x)^2 + 4= 0$ $2x^4 - 576 + 4x^2 = 0$ $2(x^4 + 2x^2 - 288) = 0$ $2(x^2 - 16)(x^2 + 18) = 0$ $x = 4, -4$ Substitute the values into the equation $4y =24$ $y = 6$ $-4y = 24$ $y = -6$ All solutions: $(4, 6)$ $(-4, -6)$