Question

Решите неравенство :)

Answer 1

√f(x) ≤ g(x)   ⇔ f(x) ≥ 0

                           g(x) ≥ 0

                           f(x) ≤ g²(x)

√(x - 2)(2x - 5) ≤ x - 2

(x - 2)(2x - 5) ≥ 0

++++++ [2] ------------- [2.5] +++++++

x ∈ (-∞,2] U [2.5, +∞)

x - 2 ≥ 0

x ≥ 2

x ∈ {2} U [2.5, +∞)

(x - 2)(2x - 5) ≤ (x - 2)²

(x - 2)(2x - 5) - (x - 2)² ≤ 0

(x - 2)*(2x - 5 - x + 2) ≤ 0

(x - 2)(x - 3) ≤ 0

++++++[2] ----------- [3] +++++++++

x ∈ [2, 3]

пересекаем с x ∈ {2} U [2.5, +∞)

получаем x ∈ {2} U [2.5, 3]