This is too Difficult for Me!
3 x 2 + 3 x + 3 + 3 2 x 2 + 3 x + 2 = 6 x 2 + 1 2 x + 8
What is the sum of all values of x such that the above equation is satisfied.
The answer is -1.
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1 solution
Can you explain the steps please
It is not too clear to me how you applied CS. Can you add more details?
I believe that the inequalities are more clearly explained by saying that you applied AM-GM on ( x 2 + 3 x + 3 ) , 1 , 1 and ( 2 x 2 + 3 x + 2 ) , 1 , 1 (and we can easily check that the quadratics are always positive).
This is an interesting approach, I wonder if there is a shorter approach.
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Yes. As you said, I applied on ( x 2 + 3 x + 3 ) , 1 , 1 and ( 2 x 2 + 3 x + 2 ) , 1 , 1 . Actually, this is a problem in a magazine. I will post the better solution from this magazine when it is available.
So − 1 is the answer.