A) 45
B) 47
C) 49
D) 50
E) 51
Correct Answer: B
Solution :
Given\[\alpha \]and\[\beta \]are the roots of\[{{x}^{2}}-7x+1=0\] \[\Rightarrow \] \[\alpha +\beta =7\] and \[\alpha \beta =1\] \[\therefore \] \[\alpha -7=\beta ,\beta -7=-\alpha \] \[\therefore \] \[\frac{1}{{{(\alpha -7)}^{2}}}+\frac{1}{{{(\beta -7)}^{2}}}=\frac{1}{{{\beta }^{2}}}+\frac{1}{{{\alpha }^{2}}}\] \[=\frac{{{\alpha }^{2}}+{{\beta }^{2}}}{(\alpha {{\beta }^{2}})}\] \[={{(\alpha +\beta )}^{2}}-2\alpha \beta \] \[=49-2=47\]
You need to login to perform this action.
You will be redirected in
3 sec
