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KVPY Sample Paper KVPY Stream-SX Model Paper-15

  • question_answer
    Let \[\alpha \] and \[\beta \] be the solutions of the quadratic equation \[{{x}^{2\text{ }}}-1154x+1=0,\] then the value of \[\sqrt[4]{\alpha }+\sqrt[4]{\beta }\] is equal to -

    A) 4

    B) 5    

    C) 6

    D) 8

    Correct Answer: C

    Solution :

    \[\alpha +\beta =1154\] and \[\alpha \beta =1\]
    \[{{(\sqrt{\alpha }+\sqrt{\beta })}^{2}}=\alpha +\beta +2\sqrt{\alpha \beta }\]
    \[=1154+2=1156={{(34)}^{2}}\]
    \[\sqrt{\alpha }+\sqrt{\beta }=34\]
    Again, \[{{({{\alpha }^{1/4}}+{{\beta }^{1/4}})}^{2}}=\sqrt{\alpha }+\sqrt{\beta }+2{{(\alpha \beta )}^{1/4}}\]
    \[=34+2=36\]
    \[{{\alpha }^{1/4}}+{{\beta }^{1/4}}=6\]


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