b: Đặt \(x^2+5x+4=a\)
\(\Leftrightarrow a=5\sqrt{a+24}\)
\(\Leftrightarrow a^2=25a+600\)
\(\Leftrightarrow a^2-25a-600=0\)
\(\Leftrightarrow\left(a-40\right)\left(a+15\right)=0\)
\(\Leftrightarrow a=-15\)
hay S=∅
giải hệ phương trình:
\(\left\{{}\begin{matrix}6\sqrt{6x^3+x^2+x-5}=\left(x-\frac{4}{x}+7\right)\left(x^2+\frac{4}{x}\right)\\2\sqrt{3x}+x+5=\left(y+1\right)^2\end{matrix}\right.\)
giải pt
a) \(\sqrt[3]{x+6}+\sqrt{x-1}=x^2-1\)
b) \(\sqrt[3]{x-9}+2x^2+3x=\sqrt{5x-1}+1\)
c) \(\sqrt{3x+1}-\sqrt{6-x}+3x^2-14x-8=0\)
d) \(\sqrt{x+1}-2\sqrt{4-x}=\frac{5\left(x-3\right)}{\sqrt{2x^2+18}}\)
e) \(x^3+5x^2+6x=\left(x+2\right)\left(\sqrt{2x+2}+\sqrt{5-x}\right)\)
giải phương trình \( \sqrt{ - { x }^{ 2 } +6x-9 \phantom{\tiny{!}}} + { x }^{ 3 } = 27 \)
\(\sqrt{ { \left( x-3 \right) }^{ 2 } \left( 5-3x \right) \phantom{\tiny{!}}} +2x= \sqrt{ 3x-5+4 \phantom{\tiny{!}}} \)
Giải pt sau :
1, \(\sqrt{x+1}+\sqrt{4-x}+\sqrt{\left(x+1\right)\left(4-x\right)}=5\)
2, \(\sqrt{x+4}+\sqrt{x-4}=2x-12+2\sqrt{x^2-16}\)
3, \(\sqrt{x+\sqrt{6x-9}}+\sqrt{x-\sqrt{6x-9}}=\sqrt{6}\)
4, \(\frac{4}{x+\sqrt{x^2+x}}-\frac{1}{x-\sqrt{x^2+x}}=\frac{3}{x}\)
5, \(\sqrt{x^2+x+4}+\sqrt{x^2+x+1}=\sqrt{2x^2+2x+9}\)
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) \(\left(x+4\right)\left(x+1\right)-3\sqrt{x^2+5x+2}=6\)
Biết \(\sqrt{3x-x^2}\) +\(\sqrt{x^2-6x=13}\) =\(\sqrt{\left(x-1\right)\left(5-x\right)}\)(1) là phương trình hệ quả của phương trình \(\sqrt{m-x}\) =\(\sqrt{x+1}\) +\(\sqrt{4-x}\). Tìm m.
A.m=1 B.m=12 C.m=9 D.Không tồn tại m.
Giải các phương trình sau:
a, \(\sqrt{3+x}+\sqrt{6-x}\) =3
b, \(\sqrt{x+4\sqrt{x-4}}+x+2+\sqrt{x-4}=8\)
c, \(\sqrt{x^2+3x+2}-2\sqrt{x^2+6x+8}+\sqrt{x^2+5x}+6\)
d, \(x^4-2x^2+2x+1=0\)
e, \(\left(x+3\right)^4+\left(x-5\right)^4=1312\)
1. Giải các phương trình sau:
a)\(\sqrt[4]{x-\sqrt{x^2-1}}+\sqrt[]{x+\sqrt{x^2-1}}=2\)
b)\(x^2-x-\sqrt{x^2-x+13}=7\)
c)\(x^2+2\sqrt{x^2-3x+1}=3x+4\)
d)\(2x^2+5\sqrt{x^2+3x+5}=23-6x\)
e)\(\sqrt{x^2+2x}=-2x^2-4x+3\)
f)\(\sqrt{\left(x+1\right)\left(x+2\right)}=x^2+3x+4\)
2. Giải các bất phương trình sau:
1)\(\sqrt{x^2-4x+5}\ge2x^2-8x\)
2)\(2x^2+4x+3\sqrt{3-2x-x^2}>1\)
3)\(\dfrac{\sqrt{-3x+16x-5}}{x-1}\le2\)
4)\(\sqrt{x^2-3x+2}+\sqrt{x^2-4x+3}\ge2\sqrt{x^2-5x+4}\)
5)\(\dfrac{9x^2-4}{\sqrt{5x^2-1}}\le3x+2\)
Giải phương trình:
1. \(x^4-6x^2-12x-8=0\)
2. \(\dfrac{x}{2x^2+4x+1}+\dfrac{x}{2x^2-4x+1}=\dfrac{3}{5}\)
3. \(x^4-x^3-8x^2+9x-9+\left(x^2-x+1\right)\sqrt{x+9}=0\)
4. \(2x^2.\sqrt{-4x^4+4x^2+3}=4x^4+1\)
5. \(x^2+4x+3=\sqrt{\dfrac{x}{8}+\dfrac{1}{2}}\)
6. \(\left\{{}\begin{matrix}4x^3+xy^2=3x-y\\4xy+y^2=2\end{matrix}\right.\)
7. \(\left\{{}\begin{matrix}\sqrt{x^2-3y}\left(2x+y+1\right)+2x+y-5=0\\5x^2+y^2+4xy-3y-5=0\end{matrix}\right.\)
8. \(\left\{{}\begin{matrix}\sqrt{2x^2+2}+\left(x^2+1\right)^2+2y-10=0\\\left(x^2+1\right)^2+x^2y\left(y-4\right)=0\end{matrix}\right.\)
