Another "how many" question

Algebra Level 4

3 x + 1 + 5 x + 4 ≥ 3 x 2 − x + 3 \large\sqrt{3x+1}+\sqrt{5x+4}\geq 3x^2-x+3 How many integer values of x x satisfy the inequality above?

1 More than 2 (still countable) 2 Infinitely many None

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P C by P C , 20, Vietnam

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1 solution

Otto Bretscher
Mar 20, 2016

We see that equality holds for x = 0 , 1 x=0,1 . Since the LHS is concave in its domain and the RHS is convex, there can be no other solutions. The answer is 2 \boxed{2} .

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