Problem: If 1−4x+4x2=01-\dfrac{4}{x}+\dfrac{4}{x^{2}}=01−x4+x24=0, then 2x\dfrac{2}{x}x2 equals
Answer Choices:
A. 111
B. 111
C. 222
D. 111 or 222
E. 111 or 222 Solution:
1−4x+4x2=(1−2x)2=0;2x=11-\dfrac{4}{x}+\dfrac{4}{x^{2}}=\left(1-\dfrac{2}{x}\right)^{2}=0 ; \dfrac{2}{x}=11−x4+x24=(1−x2)2=0;x2=1.