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SSC Quantitative Aptitude Algebra Question Bank Elementary Algebra (I)

  • question_answer
    If \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=2\,(a-b-c)-3,\]then the value of \[2a-3b+4c\]is

    A) 3

    B) 1

    C) 2

    D) 4

    Correct Answer: B

    Solution :

    [b] \[{{a}^{2}}+{{b}^{2}}{{c}^{2}}=2\,\,(a-b-c)-3\] \[\Rightarrow \]   \[({{a}^{2}}-2a+1)+({{b}^{2}}+2b+1)\] \[+\,({{c}^{2}}2c+1)=0\] \[\Rightarrow \]   \[{{(a-1)}^{2}}+{{(b+1)}^{2}}+{{(c+1)}^{2}}=0\] \[\therefore \]      \[a-1=0,\]\[b+1=0,\]\[c+1=0\] \[\Rightarrow \]   \[a=1,\]\[b=-1,\]\[c=-1\] Now,     \[2a-3b+4c=2\,(1)\,-3\,(-1)+4\,(-1)=1\]


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