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SSC Sample Paper SSC CHSL (10+2) Sample Test Paper-10

  • question_answer
    If\[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}=2(x+y+z)-3,\]then \[2x+2y+3z=?\]

    A) 3                     

    B) 4

    C) 5                     

    D) 7

    Correct Answer: D

    Solution :

    \[{{x}^{2}}+{{y}^{2}}+\text{ }{{z}^{2}}=2\left( x+y+z \right)-3\] \[\Rightarrow {{x}^{2}}+{{y}^{2}}+{{z}^{2}}-2x-2y-2z+3=0\] \[\Rightarrow {{x}^{2}}-2x+1+{{y}^{2}}-2y+1+{{z}^{2}}-2z+1=0\] \[\Rightarrow {{(x-1)}^{2}}+{{(y-1)}^{2}}+{{(z-1)}^{2}}=0\] \[\therefore \]\[x-1=0\Rightarrow x=1\] \[y-1=0\Rightarrow y=1\] \[z-1=0\Rightarrow z=1\] \[\therefore \,\,2x\,+2y+3z=2+2+3=7\]


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