5. (a) Show that x2 – 5 does not have a zero in Q[/2]. (b) Prove that Q[/2] is not isomorphic to Q[/5].

Let f(n) and g(n) be functions satisfying  f(n) = {sqrt (n), 1 + f(n+1)} if sqrt (n) is an integer otherwise and g(n) = {sqrt (n), 2 + g(n+2)} if sqrt (n) is an integer othersiwe for postiive integers n. Find the least positive integer n such that f(n)/g(n) = 4/7

5. (10 points) Prove that for all positive real numbers x and y, one has the inequality +2 > 2 nool numbers satisfying (x- 3)2 + (y +1)2 < 4.

Let f(x)= 4x+x+8x. To Save yo 3 +12x+ fime factoring, also know f(x)=4x(x+i)(x+2). The of f is given graph we below (No markings on graph)- Evalvate the definite of integral f on トスッ].