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Algebra

by harsh.champ » Thu Feb 04, 2010 5:48 am
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
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by ajith » Thu Feb 04, 2010 6:22 am
harsh.champ wrote: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
Always borrow money from a pessimist, he doesn't expect to be paid back.
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by harsh.champ » Thu Feb 04, 2010 6:26 am
ajith wrote:
harsh.champ wrote: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??
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