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SSC Sample Paper SSC CGL - Sample Paper-29

  • question_answer
    If \[x={{(a+\sqrt{{{a}^{2}}+{{b}^{3}}})}^{1/3}}+{{(a-\sqrt{{{a}^{2}}+{{b}^{3}}})}^{\frac{1}{3}}},\] then what is the value of \[{{x}^{3}}+3bx-2a?\]

    A) \[2{{a}^{3}}\]                        

    B) \[-2{{a}^{3}}\]

    C) 1                                 

    D) 0

    Correct Answer: D

    Solution :

    Given, \[x={{(a+\sqrt{{{a}^{2}}+{{b}^{2}}})}^{1/3}}+{{(a-\sqrt{{{a}^{2}}+{{b}^{3}}})}^{1/3}}\] On cubing both sides, we get \[{{x}^{3}}=(a+\sqrt{{{a}^{2}}+{{b}^{3}}})+(a-\sqrt{{{a}^{2}}+{{b}^{3}}})\] \[+\,3{{(a+\sqrt{{{a}^{2}}+{{b}^{3}}})}^{1/3}}{{(a-\sqrt{{{a}^{2}}+{{b}^{3}}})}^{1/3}}\] \[\Rightarrow \] \[{{x}^{3}}=2a-3b(x)\] \[\Rightarrow \] \[{{x}^{3}}+3bx-2a=0\]


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