\(x+\sqrt{x-1}=13\)<=> \(\sqrt{x-1}=13-x\)
<=>\(\begin{cases}13-x\ge0\\x^2-27x+170=0\end{cases}\)
<=> \(\begin{cases}x\le13\\x=10,x=17\end{cases}\)
=> x=10
vậy nghiemj x=10
giải hệ pt:
\(\left\{{}\begin{matrix}\sqrt{x^2-x-y}=\frac{y}{\sqrt[3]{x-y}}\\2\left(x^2+y^2\right)-2\sqrt{2x-1}=13\end{matrix}\right.\)
giải hệ pt :
\(\left\{{}\begin{matrix}\dfrac{\sqrt{x}}{1+\sqrt{1-x}}-\dfrac{\sqrt{y}}{1+\sqrt{y}}+x+y=1\\8x^2+7x+20y-13=\left(1+\dfrac{1}{1-y}\right)\sqrt[3]{3x^2-2}\end{matrix}\right.\)
a) Giải pt: \(x+2\sqrt{7-x}=2\sqrt{x-1}+\sqrt{-x^2+8x-7}+1\)
b)Giải hệ pt \(\left\{{}\begin{matrix}xy-y^2+2y-x-1=\sqrt{y-1}-\sqrt{x}\\3\sqrt{6-y}+3\sqrt{2x+3y-7}=2x+7\end{matrix}\right.\)
giải pt \(\sqrt{x-\dfrac{1}{x}}+\sqrt{1-\dfrac{1}{x}}=x\)
giải pt
a) \(\sqrt{2x+3}+\sqrt{4-x}=6x-3\left(\sqrt{2x+3}-\sqrt{4-x}\right)^2-10\)
b) \(\sqrt{4x+1}+2\sqrt{1-x}+10\sqrt{-4x^2+3x+1}=13\)
c) \(\left(x^2+1\right)^2=13-x\sqrt{2x^2+4}\)
d) \(\left(\sqrt{x+1}+\sqrt{x-1}\right)^2-3=\frac{1}{\sqrt{x+1}-\sqrt{x-1}}\)
e) \(\left(\frac{2x-3}{\sqrt{x^2-1}}+2\right)\left(\frac{1}{\sqrt{x-1}}-\frac{1}{\sqrt{x+1}}\right)=\frac{1}{x^2-1}\)
Giải pt : 2$\sqrt{x+1}$ - $\sqrt{2x-5}$ = 6 - x
Giải pt
\(11\sqrt{4-x}-26=-7x+2\sqrt{1+x}+\sqrt{4+3x-x^2}\)
1)Tìm m để pt sau có nghiệm
\(\sqrt{x}-\sqrt{x-1}>m\left(m>0\right)\)
2) giải hệ phương trình
\(\left\{{}\begin{matrix}\dfrac{17-x^2}{y}=\sqrt{x}\left(3\sqrt{x}+1\right)+2\sqrt{63-14x-18y}\\x\left(x^2+2x+9\right)+12y=34+2\left(13-3y\right)\sqrt{17-6y}\end{matrix}\right.\)
Giải pt
\(\sqrt{x-2}+\sqrt{4-x}=2x^2-5x-1\)
