Question 32

If $$l + m + n = 9$$ and $$l^2 + m^2 + n^2 = 31$$, then the value of lm + mn + nl will be

Solution

Given : $$l + m + n = 9$$

Squaring both sides, we get :

=> $$(l + m + n)^2 = (9)^2$$

=> $$(l^2+m^2+n^2)+2(lm+mn+nl)=81$$

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

=> $$2(lm+mn+nl)=81-31=50$$

=> $$lm+mn+nl=\frac{50}{2}=25$$

=> Ans - (C)

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