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27. Find three consecutive positive integers whoseproduct is equal to sixteen times their sum.OR |
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Answer» Let m,(m + 1),(m + 2) be the consecutive integers. As per given condition,m(m + 1)(m+2) = 16(m+m+1+m+2)(m²+2m)(m+1) = 16(3m+3)(m²+2m)(m+1) = 48(m+1)m² + 2m = 48m² + 2m - 48 = 0m² + 8m - 6m - 48 = 0m(m + 8) - 6(m + 8) = 0(m + 8)(m - 6) = 0 m = -8 OR. m = 6 (m) is positive integer, so m≠-8, thus m=6 THEREFORE, THE POSITIVE INTEGERS AREm = 6m + 1 = 6 + 1 = 7m + 2 = 6 + 2 = 8 i.e., 6,7,8 are the consecutive positive integers. |
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