question_answer

If \[a+b+c=10\] and \[ab+bc+ac=31,\] then the value of \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}\] is

A)  28                   

B)  100

C)  62                   

D)         38

Correct Answer: D

Solution :

\[\because \] \[{{(a+b+c)}^{2}}={{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2ab+2bc+2ca\] \[\therefore \,\]    \[{{(10)}^{2}}=({{a}^{2}}+{{b}^{2}}+{{c}^{2}})+2(31)\] \[\Rightarrow \]   \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=100-62\] \[\Rightarrow \]   \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=38\] Sol. (Q. Nos. 16 ? 18)