How do I do the second part of this proof? I cannot manipulate to get the correct answer!

The second part is to prove (y-?)^2 ? x in the same manner like the first part. Please show me the detailed explanation.

Theorem 1.8 Let x be a positive real number. Then there is a positive real Similarly, if it were the case that y2 > a: then we set a = (y2 1)/[4(1+1)]. A number 11 such that 1'2 = y , y = I. calculation like the one we just did (see Exercise 5) then shows that (ys)2 2 1. Hence y e is also an upper bound for S, and y is therefore not the least upper Proof: We will use throughout this proof the fact that, if 0 0 and 52(1}. Then S is not empty since 1/2 E S if a: 0 and (y+)2 = 534241-6412 _ 2 _ 2 _ 2 _ y2+2 yi i,i 4(r+1) 4(:c+1) 4(a:+1) Z 2 2 2 -y 1-y I y 2 ._ _.