CMO 1972 Problem 7

a) Prove that the values of $x$ for which $x=(x^2+1)/198$ lie between $1/198$ and $197.99494949\cdots$ .

b) Use the result of problem a) to prove that $\sqrt{2}<1.41\overline{421356}$ .

c) Is it true that $\sqrt{2}<1.41421356$ ?