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JCECE Engineering JCECE Engineering Solved Paper-2004

  • question_answer
    If\[x=3+i\], then\[{{x}^{3}}-3{{x}^{2}}-8x+15\]is equal to:

    A) \[45\]                                   

    B) \[-15\]

    C) \[10\]                                   

    D)  \[6\]

    Correct Answer: B

    Solution :

    Given,\[x=3+i\] \[\therefore \]  \[{{x}^{3}}-3{{x}^{2}}-8x+15\]                 \[={{(3+i)}^{3}}-3{{(3+i)}^{2}}-8(3+i)+15\]                 \[={{3}^{3}}+3\times {{3}^{2}}\times i+3\times 3\times {{i}^{2}}+{{i}^{3}}\]                 \[-3(9+{{i}^{2}}+6i)-24-8i+15\]                 \[=27+27i-9-i-27+3-18i\]                 \[-24-8i+15\]                 \[=-15\]


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