Final answer:
The statement is false because substituting the line's equation into the circle's equation yields a quadratic equation with real solutions, indicating that the line and circle intersect.
Step-by-step explanation:
The student's question is asking whether it is true or false that no point inside the circle defined by the equation (x - 3)² + y² = 6 is on the line y = x + 1. To solve this, we can substitute y from the line's equation into the circle's equation and see if we can find valid points that satisfy both equations.
Substituting y from the line's equation into the circle's equation gives us:
(x - 3)² + (x + 1)² = 6
Expanding and simplifying, we find:
2x² - 4x - 2 = 0
Dividing all terms by 2 gives us:
x² - 2x - 1 = 0
This is a quadratic equation that can yield real solutions for x, which means that the line and the circle intersect at two points. Therefore, there are points inside the circle that lie on the line, which makes the statement false.