Violympic toán 8
Các câu hỏi tương tự
CMR vs mọi n thì :
a, ( n2 + 3n -1 ) ( n + 2 ) - n3 + 5 ⋮ 5
b, ( 6n + 1 ) ( n + 5 ) - ( 3n + 5 ) ( 2n - 1 ) ⋮ 2
c, xn ( x = 1 ) + xn ( y - 1 ) ⋮ 13 ( x,y ∈ N, x + y ⋮ 13 )
d, ( 2x2 + x ) ( 2y2 - y ) - xy ( 4 xy - 1 ) ⋮ 2
e, ( xy - 1 ) ( x2003 + y2003 ) - ( xy + 1 ) ( x2003 - y2003 )
Cho \(\left|x\right|\ge2,\left|y\right|\ge2\) . Chứng minh rằng phương trình \(\frac{xy}{x+y}=\frac{2003}{2004}\) vô nghiệm
1) Tìm số dư khi chia 19992001cho 31
2) Chứng minh \(1924^{2003^{2004^n}}+1920⋮124\)∀ \(n\ge1\)
bài 2: giải các phương trình sau:
a. x -23/24 +x-23/25 = x -23/26 +x - 23/27
b. (x +2/98 +1) +(x +3/97 +1)=(x +4/96 +1) +(x +5/95 +1)
c. x+1/2004 + x+2/2003= x+3/2002 +x+4 /2001
d. 201 -x/99 + 203 -x/97 +205 -x/95 +3 =0
Giải các phương trình sau:
a) (x2+x)2+ 4(x2+x)=12
b) \(\dfrac{x+1}{2008}\)+\(\dfrac{x+2}{2007}\)+\(\dfrac{x+3}{2006}\)=\(\dfrac{x+4}{2005}\)+\(\dfrac{x+5}{2004}\)+\(\dfrac{x+6}{2003}\)
a) frac{x-23}{24}+frac{x-23}{25}frac{x-23}{26}+frac{x-23}{27} b) frac{x+1}{2004}+frac{x+2}{2003}frac{x+3}{2002}+frac{x+4}{2001}
d) frac{x+1}{9}+frac{x+2}{8}frac{x+3}{7}+frac{x+4}{6}
c) frac{x-45}{55}+frac{x-47}{53}frac{x-55}{45}+frac{x-53}{47}
Đọc tiếp
a) \(\frac{x-23}{24}+\frac{x-23}{25}=\frac{x-23}{26}+\frac{x-23}{27}\) b) \(\frac{x+1}{2004}+\frac{x+2}{2003}=\frac{x+3}{2002}+\frac{x+4}{2001}\)
d) \(\frac{x+1}{9}+\frac{x+2}{8}=\frac{x+3}{7}+\frac{x+4}{6}\)
c) \(\frac{x-45}{55}+\frac{x-47}{53}=\frac{x-55}{45}+\frac{x-53}{47}\)
Cmr pt \(x^{15}+y^{15}+z^{15}=19^{2003}+7^{2003}+9^{2003}\) không có nghiệm nguyên
CMR:
a, 5^2005+5^2003 chia hết cho 13
b, a^2+b^2+1 lớn hơn hoặc bằng ab+a+b
c, cho a+b+c.CM:a^3+b^3+c^3=3abc
Bài 7: Giải các phương trình sau :
a) \(\frac{x+1}{9}+\frac{x+2}{8}=\frac{x+3}{7}+\frac{x+4}{6}\)
b) \(\frac{x+2}{98}+\frac{x+4}{96}=\frac{x+6}{94}+\frac{x+8}{92}\)
c) \(\frac{2-x}{2002}-1=\frac{1-x}{2003}-\frac{x}{2004}\)
d) \(\frac{x^2-10x-29}{1971}+\frac{x^2-10x-27}{1973}=\frac{x^2-10x-1971}{29}+\frac{x^2-10x-1973}{27}\)