\(\Leftrightarrow2\sqrt{\left(x^2+1\right)\left(x^4-x^2+1\right)}=3\left(x^4+2\right)\)
Đặt \(\left\{{}\begin{matrix}\sqrt{x^4-x^2+1}=a>0\\\sqrt{x^2+1}=b>0\end{matrix}\right.\)
\(\Rightarrow2ab=3\left(a^2+b^2\right)\)
\(\Leftrightarrow2\left(a^2+b^2\right)+\left(a-b\right)^2=0\)
Pt vô nghiệm
Giải pt: \(\sqrt[3]{\left(x-1\right)^2}-\sqrt[3]{\left(x+1\right)^2}=2\sqrt[3]{x^2-1}\)
Giải pt:
a)\(\sqrt{\left(4-x\right).\left(6+x\right)}=x^2-2x-12\)
b)(x+1).(x+4)=5.\(\sqrt{x^2+5x+28}\)
c)x(x+5)=2.\(\sqrt[3]{x^2+5x-2}-2\)
d)3\(\sqrt{x}+\dfrac{3}{2\sqrt{3}}=2x+\dfrac{1}{2x}-7\)
giải pt: \(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1\)
làm thế này mà chả hiểu sao lại bị gạch, ai biết chỉ với, cảm ơn nak:
+ ĐK:\(\left\{{}\begin{matrix}x\ge1\\x+3-4\sqrt{x-1}\ge0\\x+8-6\sqrt{x-1}\ge0\end{matrix}\right.\) \(\Leftrightarrow x\ge1\)
+ pt đã cho \(\Leftrightarrow\sqrt{\left(\sqrt{x-1}-2\right)^2}+\sqrt{\left(\sqrt{x-1}-3\right)^2}=1\)
\(\Leftrightarrow\left|\sqrt{x-1}-2\right|+\left|\sqrt{x-1}-3\right|=1\) (*)
Th1: \(\left\{{}\begin{matrix}\sqrt{x-1}-2< 0\\\sqrt{x-1}-3< 0\end{matrix}\right.\)
(*) \(\Leftrightarrow2-\sqrt{x-1}+3-\sqrt{x-1}=1\Leftrightarrow2\sqrt{x-1}=4\Leftrightarrow\sqrt{x-1}=2\Leftrightarrow x=5\left(N\right)\)
Th2: \(\left\{{}\begin{matrix}\sqrt{x-1}-2\ge0\\\sqrt{x-1}-3\ge0\end{matrix}\right.\)
(*) \(\Leftrightarrow\sqrt{x-1}-2+\sqrt{x-1}-3=1\Leftrightarrow2\sqrt{x-1}=6\Leftrightarrow\sqrt{x-1}=3\Leftrightarrow x=10\left(N\right)\)
Th3: \(\sqrt{x-1}-3< 0\le\sqrt{x-1}-2\)
(*) \(\Leftrightarrow\sqrt{x-1}-2+3-\sqrt{x-1}=1\Leftrightarrow1=1\left(đúng\right)\)
Kl: \(x\ge1\)
giải pt
\(x^3+x+6=2\left(x+1\right)\sqrt{3+2x-x^2}\)
giải pt: \(\left(x+1\right)\sqrt{2\left(x^2+4\right)}=x^2-x-2\)
giải hệ pt:
\(\left\{{}\begin{matrix}\frac{1}{\sqrt{x}}-\frac{\sqrt{x}}{y}=x^2+xy-2y^2\\\left(\sqrt{x+3}-\sqrt{y}\right)\left(1+\sqrt{x^2+3x}\right)=3\end{matrix}\right.\)
1,Giải PT
a,\(\sqrt{100.\left(x-3\right)}=\sqrt{20}\)
b,\(\sqrt{\left(x-3\right)^2}=7\)
c,\(\sqrt{4x^2+4x+1}=6\)
d,\(\sqrt{x^2-4x+4}-2x+5=0\)
e,\(\sqrt{3x^2}=x+2\)
f,\(\sqrt{x^2+6x+9}=3x-6\)
Giải pt : a) \(\sqrt{3x^2-5x+1}-\sqrt{x^2-2}=\sqrt{3\left(x^2-x-1\right)}-\sqrt{x^2-3x+4}\)
b) \(\left(x-1\right)\sqrt{x^2+5}+x=x^2+1\)
c)\(\sqrt{x+2}+2x-10=\sqrt{2x-3}\)
d)\(\sqrt{2x-3}-\sqrt{x}=2x-6\)
e) \(\sqrt{4x^2+5x+1}-2\sqrt{x^2-x+1}=9x-3\)
giải pt sau
\(\sqrt{x+3}+\sqrt{6-x}-\sqrt{\left(x+3\right)\left(6-x\right)}=3\)
