Giải phương trình \(\dfrac{3\left(x-\sqrt{3}\right)\left(x-\sqrt{5}\right)}{\left(1-\sqrt{3}\right)\left(1-\sqrt{5}\right)}+\dfrac{4\left(x-1\right)\left(x-\sqrt{5}\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}-\sqrt{5}\right)}+\dfrac{5\left(x-1\right)\left(x-\sqrt{3}\right)}{\left(\sqrt{5}-1\right)\left(\sqrt{5}-\sqrt{3}\right)}=3x-2\)
Giải hệ phương trình sau:
\(\left\{{}\begin{matrix}4\left(x+y\right)=5\left(x-y\right)\\\dfrac{40}{x+y}+\dfrac{40}{x-y}=9\end{matrix}\right.\)
Giải phương trình:
1, \(\left(x^2+x+1\right)\left(x^4+2x^3+7x^2+26x+37\right)=5\left(x+3\right)^3\)
2, \(\left(x+1\right)^3+\left(x+3\right)^3+6\left(x+1\right)\left(x+7\right)\left(x+3\right)=8\left(x+2\right)^3\)
3, \(x^3+\left(x-1\right)^3+3x\left(x-1\right)\left(x^4+x\right)=\left(2x-1\right)^3\)
4, \(\dfrac{\left(x+1\right)^3}{3x+1}+\dfrac{x^3+5x+2}{x^3+2x+1}=x+3\)
5, \(\dfrac{5x^3+x^2+x+1}{4x^2+1}+\dfrac{6\left(4x^2+1\right)}{x^3+x^2+1}=x+7\)
6, \(\left(x^2-4x+1\right)^3+\left(8x-x^2+4\right)^3+\left(x-5\right)^3=125x^3\)
Bài 1: Tìm x:
a) \(\left|x+\dfrac{4}{15}\right|-\left|-3,75\right|=-\left|-2,15\right|\)
b) \(\left|\dfrac{5}{3}x\right|=\left|-\dfrac{1}{6}\right|\)
c) \(\left|\dfrac{3}{4}x-\dfrac{3}{4}\right|-\dfrac{3}{4}=\left|-\dfrac{3}{4}\right|\)
Bài 2: Tìm x,y:
a) \(\left|\dfrac{1}{2}-\dfrac{1}{3}+x\right|=\dfrac{1}{4}-\left|y\right|\)
b) \(\left|x-y\right|+\left|y+\dfrac{9}{25}\right|=0\)
Bài 3: Tìm giá trị nhỏ nhất:
a) A= \(\left|x+\dfrac{15}{19}\right|-1\)
b) B= \(\dfrac{1}{2}+\left|x-\dfrac{4}{7}\right|\)
Bài 4: Tìm giá trị lớn nhất:
a) A= 5- \(\left|\dfrac{5}{3}-x\right|\)
b) B= 9-\(\left|x-\dfrac{1}{10}\right|\)
Giải phương trình:
\(\frac{\left(x-1\right)^4}{\left(x^2-3\right)^2}+\left(x^2-3\right)^4+\frac{1}{\left(x-1\right)^2}=3x^2-2x-5\)
Giải phương trình:
1, \(\left(x+3\right)\left(3x^4+8x^2+12x+21\right)=5\left(x^2+1\right)^3\)
2, \(3\left(x^2+2x-1\right)^2-2\left(x^2+3x-1\right)^2+5x^2=0\)
3, \(\dfrac{x^2+x+1}{x+1}+\dfrac{x^2+2x+2}{x+2}-\dfrac{x^2+3x+3}{x+3}-\dfrac{x^2+4x+4}{x+4}=0\)
4, \(\left(\dfrac{x+6}{x-6}\right)\left(\dfrac{x+4}{x-4}\right)^2+\left(\dfrac{x-6}{x+6}\right)\left(\dfrac{x+9}{x-9}\right)^2=2.\dfrac{x^2+36}{x^2-36}\)
Giải PT
\(\left(x-1\right)\left(x-3\right)\left(x+5\right)\left(x+7\right)=297\)
\(x^4-8x^2+x+12=0\)
\(x^4+5x^3-10x^2+10x+4=0\)
\(\left(6x^2-5x+1\right)\left(x^2-5x+6\right)=4x^2\)
Giải hpt
\(\left\{{}\begin{matrix}\left(x-y\right)\left(x^2+y^2\right)=x^4-1\\\left(x+y\right)\left(x^4+y^4\right)=x^4+1\end{matrix}\right.\)
giải hệ phương trình:
1, \(\left\{{}\begin{matrix}2y\left(4y^2+3x^2\right)=x^4\left(x^2+3\right)\\2012^x\left(\sqrt{2y-2x+5}-x+1\right)=4024\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}x^3-2x^2y-15x=6y\left(2x-5-4y\right)\\\frac{x^2}{8y}+\frac{2x}{3}=\sqrt{\frac{x^3}{3y}+\frac{x^2}{4}}-\frac{y}{2}\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}8\left(x^2+y^2\right)+4xy+\frac{5}{\left(x+y\right)^2}=13\\2x+\frac{1}{x+y}=1\end{matrix}\right.\)
