Txd D=[1721;+∞) Ta có bpt ⇔ √2x2−x+3−(x+1) + (x2+1)−√21x−17 ≥ 0 ⇔ x2−3x+2x+1+√2x2−x+3 + x4+2x2−21x+18x2+1+√21x−17 ≥ 0 ⇔ (x2−3x+2) (1x+1+√2x2−x+3+x2+3x+9x2+1√21x−17) ≥0 ⇔ x2−3x+2≥ 0 ⇔ x≥2 hoặc x≤1Kết hợp vs D⇒1721≤x≤1 Hoặc x≥2
Txd D=[1721;+∞) Ta có bpt
⇔ √2x2−x+3−(x+1) +
(x2+1)−√21x−17 ≥ 0
⇔ x2−3x+2x+1+√2x2−x+3 +
x4+2x2−21x+18x2+1+√21x−17 ≥ 0
⇔ (
x2−3x+2) ($\frac{1}{x+1+\sqrt{2x^{2}-x+3}}+ \frac{x^{2}+3x+9}{x^{2}+1
+\sqrt{21x-17}}
)\geq
0\Leftrightarrow
x^{2}-3x+2 \geq
0\Leftrightarrow
x \geq 2
hoặc x \leq 1
KếthợpvsD \Rightarrow \frac{17}{21}\leq x\leq 1
Hoặcx\geq 2$