If (m - n) = 4 and (m³ - n³) = 1216, then find the value of (mn).
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Correct answer: B
Explanation
Given:
m − n = 4
m³ − n³ = 1216
By the formula:
m³ − n³ = (m − n)(m² + mn + n²)
1216 = 4(m² + mn + n²)
m² + mn + n² = 1216 / 4 = 304
(m − n)² = m² + n² − 2mn
4² = m² + n² − 2mn
16 = m² + n² − 2mn
m² + n² = 16 + 2mn
Now substitute in the first equation:
(m² + n²) + mn = 304
(16 + 2mn) + mn = 304
16 + 3mn = 304
3mn = 288
mn = 96