√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]
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Verified answer
√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]