求證:a2+b2+1≥ab+a+b.

求證:a2+b2+1≥ab+a+b.

證明:∵a2+b2≥2ab,a2+1≥2a,b2+1≥2b,∴把以上三個式子相加得:2(a2+b2+1)≥2(ab+a+b)∴a2+b2+1≥ab+a+b