Question

CMR: \(\left(a+b\right)\left(a^3+b^3\right)\le2\left(a^4+b^4\right)\)

Answer 1

Khá dễ!

Ta có: \(\left(a+b\right)\left(a^3+b^3\right)\le2\left(a^4+b^4\right)\)

<=> \(a^4+a^3b+ab^3+b^4\le a^4+b^4+a^4+b^4\)

<=> \(a^3b+ab^3\le a^4+b^4\)

<=> \(a^4-a^3b+b^4-ab^3\ge0\)

<=> \(a^3\left(a-b\right)-b^3\left(a-b\right)\ge0\)

<=> \(\left(a-b\right)\left(a^3-b^3\right)\ge0\)

<=> \(\left(a-b\right)^2\left(a^2+ab+b^2\right)\ge0\) (Luôn đúng)

=> đpcm

Answer 2

@Lê Văn Huy @Ace Legona @Nguyễn Huy Tú @Akai Haruma Mỹ Duyên..... giúp vs ~~ T_T pờ li :(((