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Part of 2024 Indonesia TST

Problems(2)

Absolute value, bash go brrr

Source: Indonesia 2024 TSTST - Algebra

2/29/2024
Given real numbers x,y,zx,y,z which satisfies ∣x+y+z∣+∣xy+yz+zx∣+∣xyz∣≤1|x+y+z|+|xy+yz+zx|+|xyz| \le 1 Show that max{∣x∣,∣y∣,∣z∣}≤1max\{ |x|,|y|,|z|\} \le 1.
algebrainequalitiesIndonesiaIndonesia TSTabsolute value
Second degree polynomial

Source: Indonesia TST Round 1-algebra

3/3/2024
Find all second degree polynomials P(x)P(x) such that for all a∈R,a≥1a \in\mathbb{R} , a \geq 1, then P(a2+a)≥a.P(a+1)P(a^2+a) \geq a.P(a+1)
algebrapolynomialIndonesiaIndonesia TST