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9.4

Part of IV Soros Olympiad 1997 - 98 (Russia)

Problems(3)

min 16 x^3/y+y^3/x-\sqrt{xy} (IV Soros Olympiad 1997-98 Correspondence 9.4)

Source:

6/1/2024
Find the smallest value of the expression 16⋅x3y+y3x−xy16 \cdot \frac{x^3}{y}+\frac{y^3}{x}-\sqrt{xy}
algebrainequalities
min max , nested absolute values (IV Soros Olympiad 1997-98 R3 9.4)

Source:

6/1/2024
Find the smallest and largest values of the expression ∣...∣∣x−1∣−1∣...−1∣+1∣∣x−2∣−1∣+1\frac{ \left| ...\left| |x-1|-1\right| ... -1\right| +1}{\left| |x-2|-1 \right|+1} (The number of units in the numerator of a fraction, including the last one, is eleven, of which ten are under the absolute value sign.)
absolute valueinequalitiesalgebra
(x^2-x-1)^2-x^3=5 (IV Soros Olympiad 1997-98 R2 9.4)

Source:

6/1/2024
Solve the equation (x2−x−1)2−x3=5(x^2-x-1)^2-x^3=5
algebra