Answer to Question #228678 in Algebra for Caren

Question

, In a cartesian plane (OXY) the solution of the equation e^2x – 2e^x + 1 = 0 represent,

A.     A point

B.     A line

C.     A circle

Answer 1

The equation $e^{2x}-2e^x+1=0$ is equivalent to the equation $(e^x-1)^2=0.$ It follows that $e^x-1=0,$ and hence $e^x=1.$ We conclude that the point $x=0$ is a unique solution of the equation.

Answer: A