Question

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

Answer 1

Given :
l + m + n = 9

l²+ m² + n²= 31

l + m + n = 9

On squaring both sides

(l + m + n)²= 9²

(l²+m²+n²+2(lm+mn+nl) = 81

31 +2(lm+mn+nl) = 81

2(lm+mn+nl) = 81 - 31

2(lm+mn+nl) = 50

(lm+mn+nl) = 50/2

(lm+mn+nl) = 25

Hence, the value of (lm+mn+nl) = 25

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Hope this will help you....

Answer 2

Given :

l + m + n = 9

l²+ m² + n²= 31

l + m + n = 9

On squaring both sides

(l + m + n)²= 9²

(l²+m²+n²+2(lm+mn+nl) = 81

31 +2(lm+mn+nl) = 81

2(lm+mn+nl) = 81 - 31

2(lm+mn+nl) = 50

(lm+mn+nl) = 50/2

(lm+mn+nl) = 25

Hence, the value of (lm+mn+nl) = 25

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Hope this will help you....