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∑k=1n(x+k−1)(x+k)=10n\displaystyle \sum^{n}_{k=1}(x+k-1)(x+k)=10nk=1∑n(x+k−1)(x+k)=10n
If the above equation has α\alphaα and α+1\alpha+1α+1 as its roots. Find the value of the positive integer nnn.
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