Polynomials, inequalities, complex numbers, sequences and functional equations.
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Q1 · Algebra · MEDIUM
If x⁴ + 1/x⁴ = 47, what is the value of x² + 1/x²?
Q2 · Algebra · HARD
Find the number of real solutions to the equation x⁴ - 4x³ + 6x² - 4x + 1 = 0.
Q3 · Algebra · EASY
If p and q are positive integers such that p² + q² = 2025 and p + q = 63, find the value of pq.
Q4 · Algebra · MEDIUM
Find the number of ordered pairs (x, y) of positive integers satisfying x² - y² = 221.
Q5 · Algebra · EASY
If the polynomial x³ - 6x² + px - 8 has three positive integer roots, find the value of p.