A) \[{{\left( \frac{7}{3} \right)}^{2}}\]
B) \[{{\left( \frac{8}{3} \right)}^{2}}\]
C) \[{{\left( \frac{10}{3} \right)}^{2}}\]
D) \[{{\left( \frac{5}{3} \right)}^{2}}\]
Correct Answer: B
Solution :
\[\Rightarrow \] \[x+\frac{1}{x}=\frac{10}{3}\] squaring both sides, \[\Rightarrow \] \[{{\left( x+\frac{1}{x} \right)}^{2}}={{\left( \frac{10}{3} \right)}^{2}}\] \[={{x}^{2}}+\frac{1}{{{x}^{2}}}+2=\frac{100}{9}\] \[\Rightarrow \]\[{{x}^{2}}+\frac{1}{{{x}^{2}}}=\frac{100}{9}-2\] \[\Rightarrow \]\[{{x}^{2}}+\frac{1}{{{x}^{2}}}=\frac{82}{9}\] Now, subtracting 2 both side, \[\Rightarrow \]\[{{x}^{2}}+\frac{1}{{{x}^{2}}}-2=\frac{82}{9}-2\] \[={{\left( x-\frac{1}{x} \right)}^{2}}=\frac{64}{9}\] \[\therefore \]\[{{\left( x-\frac{1}{x} \right)}^{2}}={{\left( \frac{8}{3} \right)}^{2}}\]
You need to login to perform this action.
You will be redirected in
3 sec
