If l + m + n = 9 and l2 + m2 + n2 31, then the value of

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If l + m + n = 9 and l² + m² + n² 31, then the value of (lm + mn + nl) will be

1. 22
2. 50
3. 25
4. –25

Correct Option: C

l² + m² + n² 31
l + m + n = 9
On squaring both sides,
(l + m + n)² = 81
⇒ l² + m² + n² + 2 (lm + mn + nl) = 81
⇒ 31 + 2(lm + mn + nl) = 81
⇒ 2(lm + mn + nl) = 81 – 31 = 50

⇒ lm + mn + nl =	50	= 25
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