Đặt \(\sqrt{x^2+1}=a\ge1\Rightarrow x^2=a^2-1\)
\(\left(4x-1\right)a=2\left(a^2-1\right)+2x+1\)
\(\Leftrightarrow2a^2-\left(4x-1\right)a+2x-1=0\)
\(\Leftrightarrow2a^2-a-2\left(2x-1\right)a+2x-1=0\)
\(\Leftrightarrow a\left(2a-1\right)-\left(2x-1\right)\left(2a-1\right)=0\)
\(\Leftrightarrow\left(2a-1\right)\left(a-2x+1\right)=0\)
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
\(\left\{{}\begin{matrix}2x^2+y^2-3xy+3x-2y+1=0\\4x^2-y^2+x+4=\sqrt{2x+y}+\sqrt{x+4x}\end{matrix}\right.\)
giải các PT sau :
a) \(\left|2x+3\right|-\left|x\right|+\left|x-1\right|=2x+4\)
b) \(\sqrt{x}-\dfrac{4}{\sqrt{x+2}}+\sqrt{x+2}=0\)
c) \(\sqrt{x+\sqrt{2x-1}}+\sqrt{x-\sqrt{2x-1}}=\sqrt{2}\)
d) \(x+\sqrt{x+\dfrac{1}{2}+\sqrt{x+\dfrac{1}{4}}}=4\)
e) \(\sqrt{4x+3}+\sqrt{2x+1}=6x+\sqrt{8x^2+10x+3}-16\)
f)\(\sqrt[3]{x-2}+\sqrt{x+1}=3\)
GIÚP MÌNH VỚI MÌNH ĐANG CẦN GẤP
giải hệ pt:
\(\left\{{}\begin{matrix}\sqrt{2x+y-1}-\sqrt{x+2y-2}+x-y+1=0\\4x^2-y^2+x+4=\sqrt{2x+y}+\sqrt{x+4y}\end{matrix}\right.\)
Giải pt
a) \(x^2-2x+3\sqrt{x^2-2x-3}=7\)
b) \(\left(x-2\right)^2+2=\sqrt{x^2-4x+12}\)
c) \(x^2+\sqrt{x^2+11}=31\)
d) \(\sqrt{2x^2+4x+1}=1-x\left(x+2\right)\)
e) \(\left(x+1\right)\left(x+4\right)=5\sqrt{x^2+5x+28}\)
giải pt \(x^2+\left(3-x\right)\sqrt{2x-1}=x\left(3\sqrt{2x^2-5x+2}-\sqrt{x-2}\right)\)
giải pt
a) \(\left|2x-1\right|=x+3\)
b) \(\left|4x+7\right|=2x+5\)
c) \(\left|2x^2-3x-5\right|=5x-5\)
d) \(\left|x^2-4x-5\right|=4x-17\)
e) \(\left|x-2\right|=3x^2-x-2\)
f) \(\left|4x+1\right|=x^2+2x-4\)
g) \(\sqrt{x^2+6x+9}=\left|2x-1\right|\)
Giải pt:
a) \(x\left(x-4\right)\sqrt{-x^2+4x}+\left(x-2\right)^2=2\)
b) \(\left(x^2+1\right)^2=5-x\sqrt{2x^2+4}\)
c) \(2x^2+3x-14=2\sqrt[3]{2x^2+3x-10}\)
d) \(6x^2+2x+\sqrt[3]{3x^2+x+4}-10=0\)
e) \(\left(x+4\right)\left(x+1\right)-3\sqrt{x^2+5x+2}=6\)
giai pt:
a) \(\sqrt{x^2-4x-12}=9-2x\)
b) \(\left(x+1\right)\sqrt[3]{15x^2-x-1}=x^2-1\)
c) \(\left(2x-2\right)\sqrt{2x-1}=6\left(x-1\right)\)
d) \(\frac{\sqrt{-x^2+4x-3}-1}{x-3}=2\)
e) \(\frac{5+\sqrt{x+1}}{x-2}=7\)
