Question

已知0＜a＜b＜1，求证a∧a＜b∧a

Answer 1

您好,左边通分相加,由于a,b为正数,把分母移到右边,即证a^3
b^3>=a^2b
ab^2.　　而a^3
b^3=(a
b)(a^2
b^2-ab),　右边a^2b
ab^2=(a
b)ab.　约掉因式,即证a^2
b^2-ab>=ab移项显然(a
b)^2>=0,　原式得证.