Problems And Answers PHIMO MOCK 2020 SECONDARY 3

16. Determine the exact value of \(\sqrt[3]{2 +\sqrt 5} + \sqrt[3]{2 +\sqrt 5}\).

17. Find \(x – y\), given that \(x^4 = y^4 + 24, x^2 + y^2 = 6\), and \(x + y = 3\).

18. When 29 is added to a number, it becomes a perfect square. When 100 is added to the same number, it becomes a perfect fourth power. What is the number?

19. Find the number of positive integers less than 2020 that are divisible by 16 or 20.

20. If \(A = 10^9 – 987654321\) and \(B =\frac{123456789 + 1}{10}\), what is the value of \(\sqrt{AB}\)?