Question

Xavier is attempting to recreate a problem his teacher showed him in class. To do so, he creates the table below. x y 1 3 2 ? He remembers that the slope of the line through the ordered pairs in the table was 4. What is the missing y-value in the table?

Answer 1

$\sf \: Let x=√(3+√(3+√(3+....... . .. .))) \\ \\ </p><p> \sf=>x^2=3+√(3+√(3+√(3+...........))) \\ \\ </p><p> \sf=>x^2=3+x \\ \\ </p><p> \sf=>x^2-x-3=0 \\ \\ </p><p> \sf=>x=(1±√(13))/2</p><p> \sf=>x=(1+√(13))/2$