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SSC Sample Paper Mock Test-5 SSC CGL Tear-II Paper-1

  • question_answer
    \[a+b+c=13,\]\[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=69,\]then\[(ab+bc+ca)\]is equal to      

    A)  50       

    B)  60     

    C)  55                               

    D)  45

    Correct Answer: A

    Solution :

    \[a+b+c=13\] Squaring on both sides, \[\Rightarrow \]   \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=69\] \[\Rightarrow \]\[{{(a+b+c)}^{2}}={{a}^{2}}+{{b}^{2}}+{{c}^{2}}+2ab+2bc+2ca\] \[\Rightarrow \]   \[{{(13)}^{2}}=69+2\,\,(ab+bc+ca)\] \[\Rightarrow \]\[2\,\,(ab+bc+ca)=100\] \[\Rightarrow \]   \[ab+bc+ca=\frac{100}{2}\]\[\Rightarrow \]\[ab+bc+ca=50\]                              


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