Chuyên đề Ôn thi học sinh giỏi Toán 11

CHUYÊN ĐỀ ÔN THI HỌC SINH GIỎI
Phần1- Phương trình:
1/ 5x2+3x+12-x=17x+28+3(x-13)2x-1
2/ 3x2+14x+13=x+14x+5+2(x+5)x+3
3/ 9x2+6x-83x+2+6x+23=27x2+33x+10
4/ 2x+13x+5-2x=2x+6
5/ 3x2-8x-4+2x+1x+2=23x-2
6/ x2-x-18+2x+9x+3-25x-1=0
7/ x3-5x2+13x-6=x-2x2-3x+3+23x+1
8/ 3x-4+2x+3=(1-x)(x2-2x2+3)
9/ 2x3+x2+x-1=x2x2+x+1-32x+2
10/ 5x+3=x+12x2+3-x2+33x2+5
11/ x3+6x+4=x2+3x+4+2x+1
12/ x2-2x+5+24x+5=x3-2x2+5x+4
13/ 3x+6+x-1=x2-1
14/ log3151+x+3x+4x+6x=log2x-1
15/ 3-xx-1+5-2x=-x3+10x2-34x+40
16/ 2x+51-3x+3x-10=5(x2+4x+9)210-6x+4+3x+1
17/ 9x2+24x+173x+3-x4+4x3+4x2+1x2+2x-1=x3-5x-4
18/ 1+2x-xx3-x-2-x=21+xx1+x
19/ 8x2-13x+7=1+1x33x2-2
20/ 2x2-2x30-2018.30+4x2018=30.2018
Phần 2: Hệ phương trình
Bài 1: Tìm x,y,z thỏa hệ
x2+xy+y2y2+yz+z2z2+zx+x2=xyz x4+x2y2+y4y4+y2z2+z4z4+z2x2+x4=x3y3z3
Bài 2: Giải hệ phương trình sau:
1/ x3y2+1=yy2+3y3z2+1=zz2+3z3x2+1=x(x2+3)
2/x2-2x+6.log36-y=xy2-2y+6.log36-z=yz2-2z+6.log3(6-x)=z
3/ 2015yx2+y=20162015zy2+y=20162015xz2+x=2016
4/ 2x3+3x2-18=y3+y2y3+3y2-18=z3+z2z3+3z2-18=x3+x
5/ 8sin2016x+6sin1344x-9=4sin2016y+sin672y8sin2016y+6sin1344y-9=4sin2016z+sin672z8sin2016z+6sin1344z-9=4sin2016x+sin672x; với x,y,z∈0;π
6/ 2log23x+3log22x-18=log33y+5+log3y+5 2log33(y+5)+3log32(y+5)-18=log43z+12+log4(z+12)2log43z+12+3log42z+12-18=log23x+log2x 
7/ ey2016-x2016=x2016+1y2016+1 3log2x+2y+6=2log2x+y+2+1
8/ 22x+13+2x=2y-3y-2-14x+2+2y+4=6 
9/ 2y3+2x1-x=31-x-yy=2x2-1+2xy1+x 
10/ x3-y3-2=3x-3y2x2+1-x2-32y-y2+2=0
11/ x+x2-2x+2=3y-1+1y+y2-2y+2=3x-1+1
12/
Phần 3: Bất phương trình
1/ log4x2-x-8≤1+log3x
2/ 5x-2+x-3x2+5x+63x-1-1≥0
3/ x5+2x3-8-x+6log13x+5+2x2-4x+3>0
4/ x3-x2+1x2+3+x4-x3+x-3xx-12+1-1x+x2+1≤0
5/ xx+12≥2-x-x2+2x+4x+1+x2+2x+4