A) 4
B) 6
C) 7
D) 8
Correct Answer: A
Solution :
Let \[y={{x}^{2}}-6x+13\Rightarrow {{x}^{2}}-6x+13-y=0\] Its discriminant \[D\ge 0\Rightarrow 36-4(13-y)\ge 0\] Þ\[36-52+4y\ge 0\Rightarrow 4y\ge 16\Rightarrow y\ge 4\] Hence y is not less than 4. Aliter: \[{{x}^{2}}-6x+13={{(x-3)}^{2}}+4\] Obviously the minimum value is 4.
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