giai phuong trinh \(\sqrt{x^2-2x+1}+\sqrt{x^2-4x+4}=\sqrt{1+2005^2+\dfrac{2005^2}{2006^2}}+\dfrac{2005}{2006}\)

giai he phuong trinh \(\left\{{}\begin{matrix}\dfrac{4}{x+y-1}-\dfrac{5}{2x-y+3}=\dfrac{5}{2}\\\dfrac{3}{x+y-1}-\dfrac{1}{2x-y+3}=\dfrac{7}{5}\end{matrix}\right.\)

tim nghiem nguyen duong cua phuong trinh \(\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{7}\)

giai he phuong trinh \(\left\{{}\begin{matrix}x+y=1\\x^5+y^5=11\end{matrix}\right.\)

cho \(a^3+b^3+c^3=3abc\) voi a,b,ckhac 0 va \(a+b+c\ne0\)

Tinh P=\(\left(2008+\dfrac{a}{b}\right)\left(2008+\dfrac{b}{c}\right)\left(2008+\dfrac{c}{a}\right)\)

tim gia tri lon nhat

cua bieu tthuc \(M=\dfrac{x^2}{x^4+x^2+1}\)

tim nghiem nguyen duong \(x^3y+xy^3-3x-3y=17\)

giai he phuong trinh \(\left\{{}\begin{matrix}\dfrac{4}{x+y-1}-\dfrac{5}{2x-y+1}=\dfrac{5}{2}\\\dfrac{3}{x+y-1}-\dfrac{1}{2x-y+3}=\dfrac{7}{5}\end{matrix}\right.\)

cho a, b,c duong va a+b=c=1

chumg minh \(\sqrt{a+b}+\sqrt{b+c}+\sqrt{c+a}\le\sqrt{6}\)