Please write a simple proof to show that (n^2) = n^2 + -n + 5*sqrt(n) by using the definition of big-Theta or the definition of

Please write a simple proof to show that Θ(n^2) = n^2 + -n + 5*sqrt(n) by using the definition of big-Theta or the definition of big-O twice.

Definition of big-Theta:

  

1. Use the definition of big-Theta to prove that n+n+5n = O(n). (You may either use the definition of big-Theta, as listed in the book, or use the definition of big-O twice.) [8