Final answer:
The slope of the line tangent to the equation x²+xy-y²=1 at the point (2,3) is 7/4.
Step-by-step explanation:
The equation x²+xy-y²=1 can be rewritten as y²-xy-x²=-1. To find the slope of the line that is tangent to this equation at the point (2,3), we need to take the derivative of the equation and evaluate it at that point.
Taking the derivative of the equation with respect to x, we get 2y·dy/dx - y - 2x·dx/dy = 0. Solving for dy/dx, we find dy/dx = (y+2x)/(2y-x).
Substituting the coordinates (2,3) into the equation, we get dy/dx = (3+4)/(6-2) = 7/4.