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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 \[4a-3b+5c\]is

    A) 2

    B) 3

    C) 5

    D) 6

    Correct Answer: A

    Solution :

    [a] \[{{a}^{2}}+{{b}^{2}}+{{c}^{2}}=2(a-b-c)-3\] \[\Rightarrow \]\[{{a}^{2}}-2a+1+{{b}^{2}}+2b+1+{{c}^{2}}+2c+1=0\] \[\Rightarrow \]\[{{(a-1)}^{2}}+{{(b+1)}^{2}}+{{(c+1)}^{2}}=0\] \[\Rightarrow \]\[{{(a-1)}^{2}}=0,\]\[{{(b+1)}^{2}}=0,\]\[{{(c+1)}^{2}}=0\] \[\Rightarrow \]\[a=1,\]\[b=-1,\]\[c=-1\] \[\therefore \]\[4a-3b+5c=4+3-5=2\]


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