ĐK: \(x\ge-1\)
PT \(\Leftrightarrow\sqrt{3x+7}=2+\sqrt{x+1}\)
\(\Leftrightarrow3x+7=5+x+4\sqrt{x+1}\)
\(\Leftrightarrow2x+2=4\sqrt{x+1}\) \(\Leftrightarrow x+1=2\sqrt{x+1}\)
\(\Leftrightarrow x^2+2x+1=4x+4\)
\(\Leftrightarrow x^2-2x-3=0\) \(\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-1\end{matrix}\right.\) (TM)
Vậy phương trình có tập nghiệm \(S=\left\{-1;3\right\}\)
1.Giai pt bang cach dat an phu :
a, 3x + 14 + 5\(\sqrt{x-2}\) = 7(\(\sqrt{x+1}+\sqrt{x^2-x-2}\) )
b, 7\(\sqrt{3x-7}\) +(4x-7)\(\sqrt{7-x}\) =32
Giải phương trình
a, \(x+1+2\sqrt{7-x}-2\sqrt{x+1}=\sqrt{7+6x-x^2}\)
b, \(4x^2+3x+3=4\sqrt{x^3+3x^2}+2\sqrt{2x-1}\)
c, \(\sqrt{x}-\sqrt{x+1}-\sqrt{x+4}+\sqrt{x+9}=0\)
d, \(3x^2+4x+10=2\sqrt{14x^2-7}\)
Giải phương trình:
1, \(3x^2+6x-3=\sqrt{\dfrac{x+7}{3}}\) (2 cách khác nhau )
2, \(\left(\sqrt{3x+1}-\sqrt{x-2}\right)\left(\sqrt{3x^2+7x+2}+4\right)=4x-2\)
3, \(\sqrt{-3x-1}+\sqrt{9x^2+9x+3}=-9x^2-6x\)
4, \(\sqrt{x^2+x-6}+3\sqrt{x-1}=\sqrt{5x^2-1}\)
5, \(\left(\sqrt{x+4}+2\right)\left(x+2\sqrt{x-5}+1\right)=6x\)
6, \(\sqrt{5-x^4}-\sqrt[3]{3x^2-2}=1\)
7, \(3x^2+11+\sqrt{x-2}+\sqrt{2x+3}=14x\)
8, \(\sqrt{x-\sqrt{x-\sqrt{x-\sqrt{x-7}}}}=7\)
9, \(\sqrt{2x^2-1}+3x\sqrt{x^2-1}=3x^3+2x^2-9x-7\) ( với \(x>0\) )
1. giải phương trình
a. \(\sqrt{2+\sqrt{3x-5}}=\sqrt{x+1}\)
b. \(\left(7-\sqrt{x}\right)\left(8-\sqrt{x}\right)=x+11\)
c. \(1+\sqrt{3x+1}=3x\)
d. \(\sqrt{\dfrac{3x+7}{x+3}}=4\)
Giai phuong trinh
1/ \(\sqrt{x^2+4x+5}+\sqrt{x^2-6x+13}=3\)
2/ \(\sqrt{3x^2-18x+28}+\sqrt{4x^2-24x+45}=6x-x^2-5\)
3/ \(\sqrt{2x^2-4x+27}+\sqrt{3x^2-6x+12}=4x^2+8x+4\)
4/ \(\sqrt{x^2+x+7}+\sqrt{x^2+x+2}=\sqrt{3x^2+3x+19}\)
5/ \(\left(x+2\right)\left(x+3\right)-\sqrt{x^2+5x+1}=9\)
6/ \(\left(x+4\right)\left(x+1\right)-3\sqrt{x^2+5x+2}=6\)
7/ \(\sqrt{2x^2+3x+5}+\sqrt{2x^2-3x+5}=3\sqrt{x}\)
Giải các pt sau:
a) \(\sqrt{x+8}+\frac{9x}{\sqrt{x+8}}-6\sqrt{x}=0\)
b) \(x^4-2x^3+\sqrt{2x^3+x^2+2}-2=0\)
c) \(3x\sqrt[3]{x+7}\left(x+\sqrt[3]{x+7}\right)=7x^3+12x^2+5x-6\)
d) \(4x^2+\left(8x-4\right)\sqrt{x}-1=3x+2\sqrt{2x^2+5x-3}\)
e) \(16x^2+19x+7+4\sqrt{-3x^2+5x+2}=\left(8x+2\right)\left(\sqrt{2-x}+2\sqrt{3x+1}\right)\)
f) \(\left(5x+8\right)\sqrt{2x-1}+7x\sqrt{x+3}=9x+8-\left(x+26\right)\sqrt{x-1}\)
g) \(\sqrt[3]{3x+1}+\sqrt[3]{5-x}+\sqrt[3]{2x-9}-\sqrt[3]{4x-3}=0\)
Giải phương trình:
1, \(x^2+2x\sqrt{x-\dfrac{1}{x}}=3x+1\)
2, \(\left(13-4x\right)\sqrt{2x-3}+\left(4x-3\right)\sqrt{5-2x}=2+8\sqrt{16x-4x^2-15}\)
3, \(7\sqrt{3x-7}+\left(4x-7\right)\sqrt{7-x}=32\)
(\(\frac{3x+\sqrt{16x}-7}{x+2\sqrt{x}-3}\)-\(\frac{\sqrt{x}+1}{\sqrt{x}+3}\)-\(\frac{\sqrt{x}+7}{\sqrt{x}-1}\))/(2-\(\frac{\sqrt{x}}{\sqrt{x}-1}\))
Giải pt:
\(\sqrt{x-1}+\sqrt{x+7}+x^2-3x-2=0\)
Giải ptrinh :
\(\dfrac{x^2}{\sqrt{3x-2}}-\sqrt{3x-2}=1-x\)
\(\sqrt{x+1}+2\left(x+1\right)=x-1+\sqrt{1-x}+3\sqrt{1-x^2}\)
\(3x^2+3x+2=\left(x+6\right)\sqrt{3x^2-2x-3}\)
