`\sqrt{x^{2}-3x+8}-1=x`
`<=>\sqrt{x^{2}-3x+8}=x+1\ (ĐK:x+1\ge0<=>x\ge -1)`
`<=>x^{2}-3x+8=(x+1)^{2}`
`<=>x^{2}-3x+8=x^{2}+2x+1`
`<=>x^{2}-x^{2}+2x+3x=8-1`
`<=>5x=7`
`<=>x=7/5\ (TM)`
Vậy `S={7/5}`
\(\left(5\right)\sqrt{x+3-4\sqrt{x-1}}\sqrt{x+8+6\sqrt{x-1}}=5\)
\(\left(6\right)2x^2+3x+\sqrt{2x^2+3x+9}=33\)
\(\left(7\right)\sqrt{3x^2+6x+12}+\sqrt{5x^4-10x^2+30}=8\)
\(\left(8\right)x+y+z+8=2\sqrt{x-1}+4\sqrt{y-2}+6\sqrt{z-3}\)
a)\(\sqrt{3x-1}=2\) c) \(\sqrt{x^2-4x+4}=3x-1\)
b)\(\sqrt{x+}=2-x\) d)\(\sqrt{x^2+4}=\sqrt{3x+8}\)
Giúp mình với cảm ơn ạ
Giải các pt vô tỉ sau
1)\(\sqrt{21-x}+1=x\)
2)\(\sqrt{8-x}+2=x\)
3)\(1+\sqrt{3x+1}=3x\)
4)\(2+\sqrt{3x-5}=\sqrt{x+1}\)
1\(\sqrt{5+2\sqrt{8}}-\sqrt{5-2\sqrt{8}}\) 2)\(\dfrac{\sqrt{x^2+2\sqrt{3x}+3}}{x^2-3}\) 3) \(\dfrac{\sqrt{x^2-5x+6}}{\sqrt{x-2}}\) 4)\(\dfrac{\sqrt{\left(x-4\right)^2}}{x^2-5x+4}\) 5) \(\dfrac{3x+1}{\sqrt{9x^2+6x+1}}\)
Giải phương trình:
a)\(\sqrt{\sqrt{5}-\sqrt{3x}}=\sqrt{8+2\sqrt{15}}\)
b)\(\sqrt{4x-20}-3\sqrt{\dfrac{x-5}{9}}=\sqrt{1-x}\)
c) \(\sqrt{4x+8}+2\sqrt{x+2}-\sqrt{9x+18}=1\)
d) \(\sqrt{x^2-6x+9}+x=11\)
e) \(\sqrt{3x^2-4x+3}=1-2x\)
f) \(\sqrt{16\left(x+1\right)}-\sqrt{9\left(x+1\right)}=4\)
g) \(\sqrt{9x+9}+\sqrt{4x+4}=\sqrt{x+1}\)
a) \(\sqrt{3x^2-5x+7}\)+\(\sqrt{3x^2+x+1}\) = 12x-12
b) \(\sqrt{x^2+33}\)+3 = 2x+\(\sqrt{x^2-12}\)
c) 3x-\(8\sqrt{x+14}\) = \(2\sqrt{2x-3}\) - 28
d) \(x^2\)+\(\sqrt{x+7}\) = 7
Giải phương trình sau:
a)\(\sqrt{x+1}-5\sqrt{\left(x+1\right)\left(8-x\right)}+\sqrt{8-x}=3\)
b)\(\sqrt{3x+1}-\sqrt{6-x}+3x^2-14x-8=0\)
a)Giải các phương trình sau bằng phương pháp đặt ẩn phụ:
1) \(x^2-3x-3=\frac{3\left(\sqrt[3]{x^3-4x^2+4}-1\right)}{1-x}\) ;2)\(1+\frac{2}{3}\sqrt{x-x^2}=\sqrt{x}+\sqrt{1-x}\)
b) Giải các phương trình sau(không giới hạn phương pháp):
1)\(2\left(1-x\right)\sqrt{x^2+2x-1}=x^2-2x-1\) ; 2)\(\sqrt{2x+4}-2\sqrt{2-x}=\frac{12x-8}{\sqrt{9x^2+16}}\)
3)\(\frac{3x^2+3x-1}{3x+1}=\sqrt{x^2+2x-1}\) ; 4) \(\frac{2x^3+3x^2+11x-8}{3x^2+4x+1}=\sqrt{\frac{10x-8}{x+1}}\)
5)\(13x-17+4\sqrt{x+1}=6\sqrt{x-2}\left(1+2\sqrt{x+1}\right)\);
6)\(x^2+8x+2\left(x+1\right)\sqrt{x+6}=6\sqrt{x+1}\left(\sqrt{x+6}+1\right)+9\)
7)\(x^2+9x+2+4\left(x+1\right)\sqrt{x+4}=\frac{5}{2}\sqrt{x+1}\left(2+\sqrt{x+4}\right)\)
8)\(8x^2-26x-2+5\sqrt{2x^4+5x^3+2x^2+7}\)
Giải phương trình:
a) \(\sqrt{4-3x}=8\)
b) \(\sqrt{4x-8}-12\sqrt{\dfrac{x-2}{9}}=-1\)
c) \(\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)=7\)
1/giải pt \(x^2+3x\sqrt[3]{3x+2}-12+\frac{1}{\sqrt{x}}=\frac{\sqrt{x}+8}{x}\)
