IMO 1960 Q2 #
For what values of the variable $x$ does the following inequality hold:
[\dfrac{4x^2}{(1 - \sqrt {2x + 1})^2} < 2x + 9 \ ?]
We follow solution at Art of Problem Solving with minor modifications.
The predicate says that x
satisfies the inequality
[\dfrac{4x^2}{(1 - \sqrt {2x + 1})^2} < 2x + 9]
and belongs to the domain of the function on the left-hand side.
The number satisfies the inequality.
The number belongs to the domain of (\sqrt {2x + 1}).
The number belongs to the domain of the denominator.
Instances For
The number belongs to the domain of (\sqrt {2x + 1}).
The number belongs to the domain of the denominator.
Solution of IMO 1960 Q2: solutions of the inequality are the numbers of the half-closed interval ([-1/2, 45/8)) except for the number zero.