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If m – n = 2 and mn = 15, (m, n > 0) then the value of (m² – n²) (m³ – n³) is :
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- 1856
- 1658
- 1586
- 1568
Correct Option: D
m – n = 2; mn = 15
∴ (m + n)² = (m – n)² + 4mn = 4 + 4 × 15 = 64
⇒ m + n = 64 = 8
∴ m + n + m – n = 8 + 2 = 10
⇒ 2m = 10 ⇒ m = 5
∴ m + n = 8 ⇒ 5 + n = 8
⇒ n = 8 – 5 = 3
∴ (m² – n²) (m³ – n³)
= (5² – 3²) (5³ – 3³)
= (25 – 9) (125 – 27)
= 16 × 98 = 1568
