- 急…数学题！设abc属于R+,且a+b=c,求证a^2/3+b^
- 设a b c属于R+,且a+b=c,求证a^2/3+b^2/3>c2/3
- 证:a b c属于R+,且a+b=c,
由基本不等式:
3a(abb)^1/3+3b(aab)^1/3>=2{[3a(abb)^1/3]*3b(aab)^1/3]}^1/2
>=2[9ab(aaabbb)^1/3]^1/2
>=6ab>2ab.
两边加(aa+bb),aa+3a(abb)^1/3+3b(aab)^1/3+bb>aa+2ab+bb
aa+3(aaaabb)^1/3+3(aabbbb)^1/3>aa+2ab+bb
[(aa)1/3+(bb)1/3]^3>(a+b)^2=cc
两边开3次方根:a^2/3+b^2/3>c2/3
得证.