Question

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In class, we noticed something interesting: (-1) 2 4 This motivates a natural question: whether or not there exist other pairs of distinct real numbers x and y such that To avoid square-roots of negatives (complex numbers), we consider only pos- itive values of a and y. We use a graph to get us started: 0.5 0,5 Figure 1: The Solution Set for y. (Graphic created with Desmos) The line y = x isn't of interest to us, instead, we focus on the curve consisting of distinct pairs of numbers. This graph suggests that the answer ax for is yes, and so we investigated algebraically. If we assume that y some positive real number a, then we have a) ar) (ax) XI-a-aa Since y ax, we have - a ara It appears that for any positive real number a A 1, we will obtain a of a, and we will use the notation (a) and y(a): (a)-a 3. Looking at the grngph, it appears thst thethe points (1,0) and (0,1). Verify this algebraically

Answer 1

ly ak tive Yea MUmbers 'pthreaches fo zero UJ R20 (0,') app.aera, На ее .cowe