x+a/b+c + x+b/c+a + x+c/a+b + 3 = 0 ,a>0,b>0,c>0
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Answered by
3
i think u r asking value of x .
hope u find it helpful.
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jac5:
impressive
Splitting the 3 into three separate 1s was a nice move.
thanks brother
Answered by
4
Answer:
x = -(a+b+c)
Step-by-step explanation:
Multiplying through by (a+b)(b+c)(c+a) gives:
(x+a)(a+b)(c+a) + (x+b)(a+b)(b+c) + (x+c)(b+c)(c+a) + 3(a+b)(b+c)(c+a) = 0
Looking at this, we realise that this would be so easy if only
x+a = -(b+c), x+b = -(c+a) and x+c = -(a+b) ... (*)
because that would make each of the first three terms equal to
-(a+b)(b+c)(c+a)
so they'd cancel with the fourth term.
Adding the three equations in (*), we want
3x + (a+b+c) = -2(a+b+c) => x = -(a+b+c).
I can't understand your first step of multiply
When there are fractions, it makes things easier if we multiply everything by the lcm of the denominators. For instance, if the equation were x/2 + x/3 = 1/5, multiply everything by (2)(3)(5) = 30 to get 15x + 10x = 6 => 25x = 6.
In this problem, the lcm of the denominators is (a+b)(b+c)(c+a) so multiply through by this. e.g.
1st term becomes: (x+a)(a+b)(b+c)(c+a)/(b+c) = (x+a)(a+b)(c+a)
With no fractions involved, things are so much simpler. On this occasion, we can almost just "see" the answer!
In this problem, the lcm of the denominators is (a+b)(b+c)(c+a) so multiply through by this. e.g.
1st term becomes: (x+a)(a+b)(b+c)(c+a)/(b+c) = (x+a)(a+b)(c+a)
With no fractions involved, things are so much simpler. On this occasion, we can almost just "see" the answer!
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