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Ta sẽ sử dụng BĐT Cauchy nh sau:
Ta có a
3
+b
3

a
2
b + ab
2



a
3
+b
3

ab(a+b)

+




+
;
Tơng tự, ta cũng có:

A






+

++

+

.
Cộng theo từng vế các BĐT trên lại với nhau ta đợc BĐT cần chứng minh.
\-*_9^Cho a, b, c là các số dơng. Chứng minh rằng:






++
+
++
+
++

[^
Ta có: a
3
+b
3

a
2
b + ab
2



a
3

+b
3
+ abc

a
2
b + ab
2
+abc



a
3
+b
3
+ abc

ab(a+b+c)
A
popo




++
=
++

++

Tơng tự , ta có:
}
po

A
po






++

++++

++
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