Question : If $l+m+n=9$ and $l^{2}+m^{2}+n^{2}=31$, then the value of $(lm+mn+nl )$ will be:
Option 1: 22
Option 2: 50
Option 3: 25
Option 4: –25
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Correct Answer: 25
Solution :
Given: $l^{2}+m^{2}+n^{2}=31$
And $l+m+n=9$
Squaring both sides,
$(l+m+n)^2=81$
⇒ $l^2+m^2+n^2+2(lm+mn+nl)= 81$
⇒ $31+2(lm+mn+nl) = 81$
⇒ $2(lm+mn+nl) = 81 – 31 = 50$
Thus, $(lm+mn+nl)=\frac{50}{2}=25$
Hence, the correct answer is 25.
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