Problem: The square of an integer is called a perfect square. If xxx is a perfect square, the next larger perfect square is
Answer Choices:
A. x+1x+1x+1
B. x2+1x^{2}+1x2+1
C. x2+2x+1x^{2}+2 x+1x2+2x+1
D. x2+xx^{2}+xx2+x
E. x+2x+1x+2 \sqrt{x}+1x+2x​+1 Solution:
Let x=n2,n⩾0;(n+1)2=n2+2n+1=x+2x+1x=n^{2}, n \geqslant 0 ;(n+1)^{2}=n^{2}+2 n+1=x+2 \sqrt{x}+1x=n2,n⩾0;(n+1)2=n2+2n+1=x+2x​+1.