[Đại số 9] - GTNN của BT

T

thutuanprocute

bai nay cung binh thuong thoi ma

dat can a=x,can b=y,can c= z
Q=x^2/(2y-5)+y^2/(2z-5)+z^2/(2x-5)
Ap dung bat dang thuc cosi voi 3 so duong:
(a+b+c)^3>=27abc
Q>=3.cac bac ba cua {[(x^2.y^2.z^2]/[(2y-5)(2z-5)(2x-5)]
Ta có:
(2y-5).5<=(2y-5+5)^2/4=y^2
(2z-5).5<=(2z-5+5)^2/4=z^2
(2x-5).5<=(2x-5+5)^2/4=x^2
Suy ra (2y-5)(2z-5)(2x-5)<=x^2.y^2.z^2/125
Suy ra Q>=3.5=15
Dau dang thuc xay ra khi va chi khi x=y=z=5

:khi (176)::khi (176)::khi (176)::khi (176)::khi (69)::khi (91):
 
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