Tìm x, y > 0 sao cho:
$(x^{2}+y+\frac{3}{4})(y^{2}+x+\frac{3}{4})=(2x+\frac{1}{2})(2y+\frac{1}{2})$
Tìm x, y > 0 sao cho:
$(x^{2}+y+\frac{3}{4})(y^{2}+x+\frac{3}{4})=(2x+\frac{1}{2})(2y+\frac{1}{2})$
Tìm x, y > 0 sao cho:
$(x^{2}+y+\frac{3}{4})(y^{2}+x+\frac{3}{4})=(2x+\frac{1}{2})(2y+\frac{1}{2})$
x2+y+3/4=x2-x+1/4+x+y+1/2=(x-1/2)2+x+y+1/2$\geq$ x+y+1/2
y2+x+3/4=y2-y+1/4+x+y+1/2=(y-1/2)2+x+y+1/2$\geq$ x+y+1/2
=> VT$\geq$(x+y+1/2)2 (x+y+1/2 > 0)
= x2+y2+2xy+x+y+1/4
VP= 4xy+x+y+1/4$\leq$x2+y2+2xy+x+y+1/4( vi x2+y2 lon hon hoac bang 2xy)
=> VP$\leq$VT
Dau "=" xay ra khi x=y=1/2
Binh chon cho minh nhe
Bài viết đã được chỉnh sửa nội dung bởi HVU: 11-02-2019 - 22:04
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