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10th Class Mathematics Related to Competitive Exam Question Bank Algebra

  • question_answer
    If \[a+b+c=0\], the value of \[\frac{{{a}^{2}}}{bc}+\frac{{{b}^{2}}}{ca}+\frac{{{c}^{2}}}{ab}\]is

    A)  1                                            

    B)  0

    C)  - 1                         

    D)         3  

    Correct Answer: D

    Solution :

     Since   \[a+b+c=0\] or            \[a+b=-c\] or            \[{{(a+b)}^{3}}=-{{c}^{3}}\] or            \[{{a}^{3}}+{{b}^{3}}+3ab(a+b)=-{{c}^{3}}\] or            \[{{a}^{3}}+{{b}^{3}}+3b(-c)=-{{c}^{3}}\] or            \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}=3abc\] Dividing both the sides by\[abc\], we get                 \[\frac{{{a}^{2}}}{bc}+\frac{{{b}^{2}}}{ac}+\frac{{{c}^{2}}}{ab}=3\]


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