设ab是非负实数,求证：a²+b²≥√(ab)(a+b)

设ab是非负实数,求证：a²+b²≥√(ab)(a+b)
设ab是非负实数,求证：a²+b²≥√(ab)(a+b)

设ab是非负实数,求证：a²+b²≥√(ab)(a+b)
a²+b²≥2ab
2(a²+b²)≥a²+b²+2ab
2(a²+b²)≥(a+b)²
a²+b²≥(a+b)²/2
(a+b)²/2≥2√(ab)(a+b)/2
a²+b²≥√(ab)(a+b)