Algebra

[harsh.champ]

If a, b, c are real numbers such that a < b <c and a + b + c = 6, ab + bc + ca = 9, then which among the following is definitely true?

(1)0 < a < 1
(2)1 < b < 3
(3)3 < c< 4
(4)All of them
(5)None of them

[ajith]

If a, b, c are real numbers such that a < b <c and a + b + c = 6, ab + bc + ca = 9, then which among the following is definitely true?

(1)0 < a < 1
(2)1 < b < 3
(3)3 < c< 4
(4)All of them
(5)None of them

I will go for b

Since if b>3 a<3 which is not possible
and if b<1 cannot satisfy the given equations

Purely hunch based

[harsh.champ]

If a, b, c are real numbers such that a < b <c and a + b + c = 6, ab + bc + ca = 9, then which among the following is definitely true?

(1)0 < a < 1
(2)1 < b < 3
(3)3 < c< 4
(4)All of them
(5)None of them

I will go for b

Since if b>3 a<3 which is not possible
and if b<1 cannot satisfy the given equations

Purely hunch based

________________
Actually,I solved the question using the equations:-
(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab+bc+ca)
and (a-b)^2 + (b-c)^2 + (c-a)^2 >0 [square is always a positive number or zero]

Can you get to the answer applying the formal technique??