Inequality 一題，20點，趕!!!

Prove the following inequality, you can use any method and theorem, thanks! ( a^2 +b^2 +c^2 )( ba^2 +cb^2 +ac^2 ) ≦ ( a^3 +b^3 +c^3 )( ab +bc +ca ) 更新: 中英文答都得~!! Kwok Victor it is not necessary to have b≦a+c, this inequality holds for all positive numbers a,b,c also, what is high inequalities theorem ??

HI, answer:b≦a+c There is NO high inequalities theorem. 數學上，不等是表明兩個對象的大小或者順序的二元關係（參見等於）。不等關係主要有四種：a < b，即 a 小於 ba > b，即 a 大於 b上述兩個屬於嚴格不等。a ≤ b，即 a 小於等於 ba ≥ b，即 a 大於等於 ba≠b，即 a 不等於 b將兩個表達式用不等符號連起來，就構成了不等式。 Inequalities are governed by the following properties. Note that, for the transitivity, reversal, addition and subtraction, and multiplication and division properties, the property also holds if strict inequality signs (< and >) are replaced with their corresponding non-strict inequality sign (≤ and ≥).TransitivityThe transitivity of inequalities states:For any real numbers, a, b, c:If a > b and b > c; then a > cIf a < b and b < c; then a < cIf a > b and b = c; then a > cIf a < b and b = c; then a < cAddition and subtractionThe properties that deal with addition and subtraction state:For any real numbers, a, b, c:If a < b, then a + c < b + c and a ? c < b ? cIf a > b, then a + c > b + c and a ? c > b ? ci.e., the real numbers are an ordered groupMultiplication and divisionThe properties that deal with multiplication and division state:For any real numbers, a, b, and non-zero cIf c is positive and a < b, then ac < bc and a/c < b/cIf c is negative and a < b, then ac > bc and a/c > b/cMore generally this applies for an ordered field, see below.Additive inverseThe properties for the additive inverse state:For any real numbers a and bIf a < b then ?a > ?bIf a > b then ?a < ?bMultiplicative inverseThe properties for the multiplicative inverse state:For any non-zero real numbers a and b that are both positive or both negativeIf a < b then 1/a > 1/bIf a > b then 1/a < 1/bIf either a or b is negative (but not both) thenIf a < b then 1/a < 1/bIf a > b then 1/a > 1/b HOPE THAT I CAN HELP YOU!!! THANKS 圖片參考：http://www.koolbadges.co.uk/images/thumbnails/i%20love%20maths-200x200.jpg

High inequalities theorem 只是亂寫一通而已。 不等式 b ≤ a + c 未必成立，例如當 a = 1, b = 8, c = 2|||||b≦a+c high inequalities theorem

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