Problem: If y=x2−2x+1+x2+2x+1y=\sqrt{x^{2}-2 x+1}+\sqrt{x^{2}+2 x+1}y=x2−2x+1+x2+2x+1, then yyy is:
Answer Choices:
A. 2x2 x2x
B. 2(x+1)2(x+1)2(x+1)
C. 000
D. ∣x−1∣+∣x+1∣|x-1|+|x+1|∣x−1∣+∣x+1∣
E. none of these Solution:
Since x2−2x+1=∣x−1∣\sqrt{x^{2}-2 x+1}=|x-1|x2−2x+1=∣x−1∣ and x2+2x+1=∣x+1∣\sqrt{x^{2}+2 x+1}=|x+1|x2+2x+1=∣x+1∣, (D) is correct.