\(\Leftrightarrow1+\dfrac{x-2}{x+1}=\dfrac{5}{2\left(x-1\right)}\)
\(\Leftrightarrow2\left(x^2-1\right)+2\left(x-1\right)\left(x-2\right)=5\left(x+1\right)\)
\(\Leftrightarrow2x^2-2+2x^2-6x+4-5x-5=0\)
\(\Leftrightarrow4x^2-11x-3=0\)
\(\Leftrightarrow4x^2-12x+x-3=0\)
=>(x-3)(4x+1)=0
=>x=3 hoặc x=-1/4
Giải phương trình:
1. \(\sqrt{2x^2+4x+7}=x^4+4x^3+3x^2-2x-7\)
2. \(\dfrac{4}{x}+\sqrt{x-\dfrac{1}{x}}=x+\sqrt{2x-\dfrac{5}{x}}\)
3. \(\dfrac{6-2x}{\sqrt{5-x}}+\dfrac{6+2x}{\sqrt{5+x}}=\dfrac{8}{3}\)
4. \(x^2+1-\left(x+1\right)\sqrt{x^2-2x+3}=0\)
5. \(2\sqrt{2x+4}+4\sqrt{2-x}=\sqrt{9x^2+16}\)
6. \(\left(2x+7\right)\sqrt{2x+7}=x^2+9x+7\)
1) \(\dfrac{x-3x^2}{2}+\sqrt{2x^4-x^3+7x^2-3x+3}=2\)
2) \(1+\sqrt{\dfrac{x-2}{1-x}}=\dfrac{2x^2-2x+1}{x^2-2x+2}\)
3) \(x+y+z+\dfrac{3}{x-1}+\dfrac{3}{y-1}+\dfrac{3}{z-1}=2\left(\sqrt{x+2}+\sqrt{y+2}+\sqrt{z+2}\right)\) với x ,y ,z > 1
4) \(\sqrt[3]{x+6}+x^2=7-\sqrt{x-1}\)
5) \(x^4-2x^3+x-\sqrt{2\left(x^2-x\right)}=0\)
giải các phương trình sau:
a,7+2x=32-3z
c,\(\dfrac{x}{3}+\dfrac{2x-6}{6}=2-\dfrac{x}{3}\)
b,\(\dfrac{x-1}{x}+\dfrac{1}{x+1}=\dfrac{2x-1}{x^2+x}\)
d,\(\dfrac{x+1}{65}+\dfrac{x+3}{63}=\dfrac{x+5}{61}+\dfrac{x+7}{59}\)
lm giúp mk đi thanks nhìu
rút gọn:
\(A=\left(\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}}{x+\sqrt{x}+1}+\dfrac{1}{1-\sqrt{x}}\right):\dfrac{\sqrt{x}-1}{2}\)
\(B=\dfrac{2x}{x+3\sqrt{x}+2}+\dfrac{5\sqrt{x}+1}{x+4\sqrt{x}-3}+\dfrac{\sqrt{x}+10}{x+5\sqrt{x}+6}\)
Tìm tập nghiệm của bất phương trình
a) \(\dfrac{x-2}{x+1}\ge\dfrac{x+1}{x-2}\)
b) \(\dfrac{\left(x-1\right)\left(2x-5\right)\left(x+1\right)}{x+4}< 0\)
Giúp mình với :
\(\dfrac{1}{2x+2+5\sqrt{x}}+\dfrac{1}{2\sqrt{x^2+4x+1}+\sqrt{x}}\)
Chứng minh nó khác 0 với ≥0
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, \(\left(\dfrac{x+6}{x-6}\right)\left(\dfrac{x+4}{x-4}\right)^2+\left(\dfrac{x-6}{x+6}\right)\left(\dfrac{x+9}{x-9}\right)^2=2.\dfrac{x^2+36}{x^2-36}\)
1/ Thực hiệm phép tính:
a) \(\left(\dfrac{x-4}{2x-4}+\dfrac{2}{x^2-2x}\right)\div\dfrac{x-2}{x+1}\)
b) \(\dfrac{2x+3}{x^2-2x+1}\div\dfrac{6x+9}{x^2-1}+\dfrac{2}{x^2-1}\)
2/ Cho a, b, c thỏa mãn \(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}=1\). Tính giá trị của biểu thức \(\dfrac{a^2}{b+c}+\dfrac{b^2}{c+a}+\dfrac{c^2}{a+b}\)
Giải:
\(\dfrac{5}{x^2}+\dfrac{2x}{\sqrt{x^2+5}}=1\)
