Do a.b.c=1 nen dat a= x/y , b= y/z , c=z/x .Thay vao de bai suy ra (a^4.b)/( a^2 +1)+ (b^4.c)/ (b^2+1) + (c^4.a)/ (c^2+1) = x^4/ {yz.(x^2+y^2)} + y^4/ {xz.(y^2+z^2) + z^4/{xy.(x^2+z^2)} => (x^2+y^2+z^2)^2 / { (x^2+y^2+z^2)^2 + (x^2.y^2+y^2.z^2+z^2.x^2)} =>2(x^2+y^2+z^2)^2 / {(x^2+y^2+z^2)^2 + (x^2+y^2+z^2)^2 /3} = 3/2 .( Do ap dung bdt bunhiacopxki )
Do
$a.b.c=1
$ nen dat
$a= x/y , b= y/z , c=z/x
$ .Thay vao de bai suy ra
$(a^4.b)/( a^2 +1)+ (b^4.c)/ (b^2+1) + (c^4.a)/ (c^2+1)
$$= x^4/ {yz.(x^2+y^2)} + y^4/ {xz.(y^2+z^2)
} + z^4/{xy.(x^2+z^2)}
$$=> (x^2+y^2+z^2)^2 / { (x^2+y^2+z^2)^2 + (x^2.y^2+y^2.z^2+z^2.x^2)}
$$=>2(x^2+y^2+z^2)^2 / {(x^2+y^2+z^2)^2 + (x^2+y^2+z^2)^2 /3} = 3/2
$ .( Do ap dung bdt bunhiacopxki )