Toán Biết a>=b>=c>0.Chứng minh a^3(b^2 – c^2)+b^3(c^2 – a^2)+c^3(a^2 – b^2) >= 0 12/07/2021 By Rose Biết a>=b>=c>0.Chứng minh a^3(b^2 – c^2)+b^3(c^2 – a^2)+c^3(a^2 – b^2) >= 0
`a>=b>=c>0` `⇒a^2>=b^2>=c^2>0` `⇒(a^2-b^2)≥0 ;(b^2-c^2)≥0;(c^2-a^2)≥0` `⇒c^3(a^2-b^2)≥0 ;a^3(b^2-c^2)≥0;b^3(c^2-a^2)≥0` `⇒c^3(a^2-b^2)≥0+a^3(b^2-c^2)≥0+b^3(c^2-a^2)≥0` Trả lời
`a>=b>=c>0`
`⇒a^2>=b^2>=c^2>0`
`⇒(a^2-b^2)≥0 ;(b^2-c^2)≥0;(c^2-a^2)≥0`
`⇒c^3(a^2-b^2)≥0 ;a^3(b^2-c^2)≥0;b^3(c^2-a^2)≥0`
`⇒c^3(a^2-b^2)≥0+a^3(b^2-c^2)≥0+b^3(c^2-a^2)≥0`