题目

Student loan (贷款) debt has become a worldwide problem. In America, the country's overall student debt reached a record of $1.6 trillion in 2019. The average person with student loan debt owed between $20,000 and $25,000. A recent Japanese government report says it has been lending over $9 billion yearly to students since 2010. Similar conditions exist in Africa and South America.Several factors account for high student loan debt. One is that employers everywhere have increased their demands for skilled workers, making higher education a requirement for many jobs. The students, however, aft（Ⅰ） 设a，b∈R+，求证：（a+b）（a2+b2）（a3+b3）≥8a3b3；（Ⅱ） 已知a≠b，求证：a4+6a2b2+b4＞4ab（a2+b2）