Grades 9-10 Video Solutions 2025-2025_9-10

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Video Summary

The problem involves finding the largest possible sum of three prime numbers whose product equals 11 times their sum. Since the product is divisible by 11, one of the primes must be 11. Denoting the other primes as \( p \) and \( q \), the equation simplifies to \( pq = 11 + p + q \). This equation shows as \( p \) and \( q \) increase, the left side grows faster than the right, implying one must be less than 5. Considering possible primes, \( p = 2 \) and \( q = 13 \) yield the maximum sum, \( 11 + 2 + 13 = 26 \). Therefore, the largest possible sum is 26.

Keywords

prime numbers

largest sum

product equation

mathematical problem

sum of primes