ĐK: \(x\le2\)
\(\sqrt{x+10}=2-x\)
\(\Leftrightarrow x+10=\left(2-x\right)^2\)
\(\Leftrightarrow x^2-4x+4-x-10=0\)
\(\Leftrightarrow x^2-5x-6=0\)
\(\Leftrightarrow\left(x-6\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=6\left(loai\right)\\x=-1\left(chon\right)\end{matrix}\right.\)
Vậy pt có nghiệm duy nhất \(x=-1\)
Cho \(A=\left(\dfrac{2}{\sqrt{x}-2}+\dfrac{3}{2\sqrt{x}+1}-\dfrac{5\sqrt{x}7}{2x-3\sqrt{2}-2}\right):\dfrac{2\sqrt{x}+3}{5x-10\sqrt{x}}\)
a. Rut gon A voi \(x>0,x\ne4\)
b. Tim x de A nguyen
cho phuong trinh:\(\dfrac{2+\sqrt{x}}{\sqrt{2}+\sqrt{2+\sqrt{x}}}+\dfrac{2-\sqrt{x}}{\sqrt{2}-\sqrt{2-\sqrt{x}}}=\sqrt{2}\)
a/tim dieu kien cua x de phuong trinh co nghia
b/giai phuong trinh
A=(\(\dfrac{x+2}{x\sqrt{x}-1}+\dfrac{\sqrt{x}}{x+\sqrt{x}+1}+\dfrac{1}{1-\sqrt{x}}\)):\(\dfrac{\sqrt{x}-1}{2}\)
Voi x≥0 va x≠1
a)Tim x de A=2/7
b)So sanh A^2va 2A
\(A=\left(\frac{1}{x-\sqrt{x}}+\frac{1}{\sqrt{x}-1}\right):\frac{\sqrt{x}+1}{\left(\sqrt{x}-1\right)^2}\)
a) ruts gon A
b) tim gtri x de \(A< \frac{1}{3}\)
Giải phương trình :
\(a,\sqrt{x+2+2\sqrt{x+1}}+\sqrt{x+10-6\sqrt{x+1}}=2\sqrt{x+2-2\sqrt{x+1}}\)
\(b,\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=x+\frac{3}{2}\)
giải phương trình
1)\(\sqrt{x+4}-\sqrt{1-x}=1\)
2)\(\left(x+3\right)\sqrt{10-x^2}=x^2-x-12\)
\(P=\dfrac{10\sqrt{x}}{x+3\sqrt{x}-4}-\dfrac{2\sqrt{x}-3}{\sqrt{x}+4}+\dfrac{\sqrt{x}+1}{1-\sqrt{x}}\) rút gọn
Tính giá trị của P = \(\left(\dfrac{\sqrt{x-1}}{3+\sqrt{x-1}}+\dfrac{x+8}{10-x}\right):\left(\dfrac{3\sqrt{x-1}+1}{x-3\sqrt{x-1}-1}-\dfrac{1}{\sqrt{x-1}}\right)\)khi x=\(\sqrt[4]{\dfrac{3+2\sqrt{2}}{3-2\sqrt{2}}}-\sqrt[4]{\dfrac{3-2\sqrt{2}}{3+2\sqrt{2}}}\)
\(\sqrt{x+1}+\sqrt{x+10}=\sqrt{x+2}+\sqrt{x+5}\)
\(\sqrt{x^2-2x+1}+\sqrt{x^2+4x+4}=2\)
\(x+4\sqrt{x+3}+2\sqrt{3-2x}+2=\sqrt{x+1}\)
\(4\sqrt{x+1}=x^2-5x+14\)
giúp mình nha :>>>
