What kind of triangle is this?
Each side of a certain triangle is multiplied with the sum of the squares of the other two sides.The sum of all such possible results is
times the product of the sides. What kind of triangle is this?
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1 solution
Analysing the given condition as mentioned in the question and with reference to the figure, we get a(b²+c²) + b(c²+a²) + c(a²+b²) = 6(a)(b)(c). Dividing the equation by (a)(b)(c), we get a/b + b/a + a/c + c/a + b/c + c/b = 6. Now we know minimum value of sum of reciprocals of positive numbers is 2 from (AM≥GM). And here it is satisfied as sum of three reciprocal pairs is 6 so each term is equal to 1. As minimum value(2) is attained at 1. Therefore, each side is 1 so it is equilateral!