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