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Hong Kong [tex]\displaystyle \sf \text{Se a, b e c s\~ao as ra\'izes da equa\c c\~ao }x^3-2x^2-3x-4=0, \\\\ \text{o valor da express\~ao } \\\\ \frac{a^5-b^5}{a-b}+\frac{b^5-c^5}{b-c}+\frac{c^5-a^5}{c-a} \\\\\ \text{\'e igual a :}[/tex] Gabarito : 183
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Peru [tex]\text{A partir de } \left\{\begin{matrix}\displaystyle \sf x+y+z=1 \\\\ \displaystyle \sf x^2+y^2+z^2 = 9 \\\\ \displaystyle \sf x^3+y^3+z^3=1 \end{matrix}\right \ .\ \text{O valor de} \displaystyle \sf\ \ \frac{4}{x^4+y^4+z^4}\ \ \text{\'e igual a :}[/tex] Gabarito : 4/33
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Trigonometria [tex]\displaystyle \sf \text{Se \ } sen^2(x) = sen(y)\cdot cos(y) \\\\ \text{ Mostre que} : \\\\ {cos(2x) = 2\cdot cos^2\left(\frac{\pi}{4}+y\right)[/tex]
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(OMA) (Argentina) [tex]\displaystyle \sf \text{Demonstre que se em um tri\^angulo ABC vale a rela\c c\~ao} : \\\\\ sen^2(A)+sen^2(B)+sen^2(C) = 2 \\\\ \text{Ent\~ao o tri\^angulo \'e ret\^angulo}[/tex]obs : A, B e C são os ângulos internos do triângulo.
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