question_answer

If \[{{x}^{2}}+2=2x,\]then the value of \[{{x}^{4}}-{{x}^{3}}+{{x}^{2}}+2\]is      [SSC (10+2) 2011]

A) \[0\]     

B) \[1\]

C) \[-\,\,1\]                        

D) \[\sqrt{2}\]

Correct Answer: A

Solution :

Given, \[{{x}^{2}}+2=2x\]

\[\Rightarrow \]\[{{x}^{2}}-2x+2=0\]

Now,

Hence, \[{{x}^{4}}-{{x}^{3}}+{{x}^{2}}+2\]can be represented as

\[=({{x}^{2}}-2x+2)({{x}^{2}}+x+1)=0\]