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Asked by sudhanshubhushanroy | 8th Nov, 2017, 01:04: PM

Expert Answer:

the space example space can space be space written space as sum from straight r equals 1 to straight n of left parenthesis straight x plus straight r minus 1 right parenthesis left parenthesis straight x plus straight r right parenthesis equals 10 straight n sum from straight r equals 1 to straight n of left parenthesis straight x squared plus 2 rx minus straight x plus straight r squared minus straight r right parenthesis equals 10 straight n nx squared plus 2 fraction numerator straight n left parenthesis straight n plus 1 right parenthesis over denominator 2 end fraction straight x minus nx plus fraction numerator straight n left parenthesis straight n plus 1 right parenthesis left parenthesis 2 straight n plus 1 right parenthesis over denominator 6 end fraction minus fraction numerator straight n left parenthesis straight n plus 1 right parenthesis over denominator 2 end fraction equals 10 straight n nx squared plus straight n squared straight x plus open parentheses fraction numerator 2 straight n plus 1 over denominator 3 end fraction minus 1 close parentheses fraction numerator straight n left parenthesis straight n plus 1 right parenthesis over denominator 2 end fraction minus 10 straight n space equals space 0 cancelling space one space straight n space from space all space and space simplifying space we space get 3 straight x plus 3 nx plus left parenthesis straight n squared minus 31 right parenthesis equals 0................ quadratic space eqn now space it space is space given space that space it space has space consecutive space integers space as space roots space so space differ e nce space of space roots space will space be space 1 difference space of space roots space is space given space by space fraction numerator square root of straight b squared minus 4 ac end root over denominator straight a end fraction space rightwards double arrow space fraction numerator square root of 9 straight n squared minus 12 straight n squared plus 372 end root over denominator 3 end fraction equals 1 rightwards double arrow space 372 minus 3 straight n squared equals 9 rightwards double arrow space straight n squared equals 121 rightwards double arrow space straight n equals 11

Answered by Arun | 7th Dec, 2017, 05:25: PM

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