1. Xet cac so thuc x,y t/m x3x+1=3y+2y. Tim max,min P=x+y.
2. Tim max,min y=(3cosx+4sinx)22(3cosx+4sinx)+5.

Đặt 3cosx+4sinx=tt[5; 5]

Khi đó (P):y=t22t+5; t[5; 5] tọa độ đỉnh của (P)I(1; 4)

Bảng biến thiên



Từ đó ta thấy maxy=40 khi t=53cosx+4sinx=5

miny=4 khi t=13cosx+4sinx=1
Bài 1:
Áp dụng BĐT: a2+b2(a+b)22(a2+b2),a,b0 ta có:
(x+y)2=9(x+1+y+2)218(x+y+3)x+y9+315
maxP=9+315{x=10+3152y=8+3152
(x+y)2=9(x+1+y+2)29(x+y+3)x+y9+3212
minP=9+3212[x=1;y=11+3212x=13+3212;y=2
làm bài 2 trước nè
đặt 3 cosx+4sinx =t.khi đó -7<= t<=7
pt lúc này là t^2-2t+5=0
lập bảng biến thiên hàm số y(t) trên đoạn [-7;7]
ta được min =4 khi t=1.max=68 khi t=-7.từ đó tìm x

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