easyQuiz已知a+b=1,a,b大于等于0,求证:a4+b4大于等于1/8

Question

easy Quiz已知a+b=1,a,b大于等于0,求证:a4+b4大于等于1/8

Answer 1

证：a+b=1大于等于二倍根号下ab.即得ab大于等于1/4 a4+b4=(a2+b2)2-2a2b2=(1-2ab)2-2a2b28 将前面得到的ab代如即证得上式a4+b4大于等于1/8