A) \[7{{x}^{2}}-6x+1=0\]
B) \[6{{x}^{2}}-7x+1=0\]
C) \[{{x}^{2}}-6x+7=0\]
D) \[{{x}^{2}}-7x+6=0\]
Correct Answer: A
Solution :
Sum of roots\[=\frac{1}{3+\sqrt{2}}+\frac{1}{3-\sqrt{2}}\] \[=\frac{3-\sqrt{2}+3+\sqrt{2}}{{{3}^{2}}-{{(\sqrt{2})}^{2}}}\] \[=\frac{6}{7}\] and multiplication of roots\[=\frac{1}{3+\sqrt{2}}\times \frac{1}{3-\sqrt{2}}\] \[=\frac{1}{9-2}\] \[=\frac{1}{7}\] \[\therefore \]Required equation is \[{{x}^{2}}-\](sum of roots) \[x+\] (multiplication of roots)\[=0\] \[\Rightarrow \] \[{{x}^{2}}-\frac{6}{7}x+\frac{1}{7}=0\] \[\Rightarrow \] \[7{{x}^{2}}-6x+1=0\]
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