已知a大于0,b大于0,且h=min(a,b/a*a+b*b)求证h小于等于根号2/2

Question

已知a大于0,b大于0,且h=min(a,b/a*a+b*b)求证h小于等于根号2/2

Answer 1

∵a^2+b^2≥2ab
∴b/(a^2+b^2)≤1/2a
令a=1/2a (a>0)
a=(根号2)/2
令a>1/2a
a>(根号2)/2
令a