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If `a+b+c=5,a^(2)+b^(2)+c^(2)=12` and `a^(3)+b^(3)+c^(3)=25`. Then the value of `a^(4)+b^(4)+c^(4)` isA. `251/6`B. `253/6`C. `255/6`D. `257/6` |
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Answer» Correct Answer - D Let `a,b,c` are the roots of equation `a_(0)x^(3)+a_(1)x^(2)+a_(2)x+a_(3)=0` Then, `s_(1)=5, s_(2)=12, s_(3)=25` Now, `a_(0)s_(1)+a_(1)=0impliesa_(1)=-5a_(0)` `a_(0)s_(2)+a_(1)s_(1)+2a_(2)=0impliesa_(2)=13/2a_(0)` `a_(0)s_(3)+a_(1)s_(2)+a_(2)s_(1)+3a_(3)=0impliesa_(3)=5/6a_(0)` `x^(3)-5x^(2)+13/2x+5/6=0` `6x^(3)-30x^(2)+39x+5=0` `implies 6x^(4)-30x^(3)+39x^(2)+5x=0` `6s_(4)-30s_(3)+39s_(2)+5s_(1)=0s_(4)=257/6` |
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