Problem: If x−1−x+1+1=0\sqrt{x-1}-\sqrt{x+1}+1=0x−1−x+1+1=0, then 4x4 x4x equals:
Answer Choices:
A. 555
B. 4−14 \sqrt{-1}4−1
C. 000
D. 1141 \dfrac{1}{4}141
E. no real value Solution:
x−1+1=x+1;∴x−1+2x−1+1=x+1\sqrt{x-1}+1=\sqrt{x+1} ; \quad \therefore x-1+2 \sqrt{x-1}+1=x+1x−1+1=x+1;∴x−1+2x−1+1=x+1. ∴2x−1=1;∴4x−4=1\therefore 2 \sqrt{x-1}=1 ; \quad \therefore 4 x-4=1∴2x−1=1;∴4x−4=1; and ∴4x=5\therefore 4 x=5∴4x=5. (This value of xxx satisfies the original equation.)