Hello, I can't seem to understand how to use continued fractions to find the value of x in: x^2 + x - 72 = 0
Can someone please explain how to solve this problem? Basically, I need to prove that x = -9 or 8.
Consider the positive solution is .
Now it means
You form the continued fraction or simply 1's so .
Now let represent the fraction (approximation) after the terms.
So and the difference between the real value is .
Now and the difference between the real value is .
This tells us the difference between the approximation and the actual value gets very close.