Ta có : \(x=\sqrt{5}+1\Rightarrow a-1=\sqrt{5}\)
\(\Rightarrow x^2-2x+1=5\)
\(\Rightarrow x^2-2x-4=0\)
Ta có : \(x^4+4x^3+x^2+6x+12\)
\(=x^4-2x^3-4x^2+6x^3-12x^2-24x-15x^2+30x-60-48\)
\(=x^2.\left(x^2-2x-4\right)+6x\left(x^2-2x-4\right)-15.\left(x^2-2x-4\right)-48=-48\)
Lại có : \(x^2-2x+12=x^2-2x-4+16=16\)
( Do \(x^2-2x-4=0\) )
Nên ta có : \(P=-\dfrac{48}{16}=-3\)
Vậy : \(P=-3\)
1.\(\sqrt{-4x^2+25}=x\)
2.\(\sqrt{3x^2-4x+3}=1-2x\)
3. \(\sqrt{4\left(1-x\right)^2}-\sqrt{3}=0\)
4.\(\dfrac{3\sqrt{x+5}}{\sqrt{ }x-1}< 0\)
5. \(\dfrac{3\sqrt{x-5}}{\sqrt{x+1}}\ge0\)
Rút gọn các biểu thức sau:
a. x+3+ \(\sqrt{x^2-6x+9}\) (x ≤ 3)
b. \(\sqrt{x^2+4x+4}-\sqrt{x^2}\) ( -2 ≤ x ≤ 0 )
c. \(\dfrac{\sqrt{x^2-2x+1}}{x-1}\) ( x > 1)
d. /x-2/ + \(\dfrac{\sqrt{x^2-4x+4}}{x-2}\) ( x < 2)
Rút gọn các biểu thức sau:
a) \(\sqrt{\dfrac{16(4x-4\sqrt{x}+1)}{6x+3\sqrt{x}}}\) với \(x > 1\)
b) \(\dfrac{\sqrt{(x)^{2}}+\sqrt{4-4x+(x)^{2}}+1}{2x-1}\) với \(x > 2\sqrt{2}\)
c) \(\sqrt{(x)^{2}-8x+16}+\sqrt{36-12x+(x)^{2}}\) với \(4< x <6\)
Giải các phương trình sau:
a) \(\sqrt{x^2-4+4}=2-x\)
b) \(\sqrt{4x-8}-\dfrac{1}{5}\sqrt{25x-50}=3\sqrt{x-2}-1\)
c) \(\sqrt{x-1}+\sqrt{9x-9}-\sqrt{4x-4}=4\)
d) \(\dfrac{1}{2}\sqrt{x-2}-4\sqrt{\dfrac{4x-8}{9}}+\sqrt{9x-18}-5=0\)
e)\(\sqrt{49-28x+4x^2}-5=0\)
f) \(\sqrt{4x-20}+\sqrt{x-5}-\dfrac{1}{3}\sqrt{9x-45}=4\)
g) x2 - 4x - 2\(\sqrt{2x-5}+5=0\)
h)\(\sqrt{3x-2}=\sqrt{x+1}\)
i) x + y + z + 8 = \(2\sqrt{x-1}+4\sqrt{y-2}+6\sqrt{z-3}\)
k) \(\sqrt{x^2-3x}-\sqrt{x-3}=0\)
l)\(\sqrt{x^2-4}+\sqrt{x-2}=0\)
m) \(4\sqrt{x+1}=x^2-5x+14\)
n) \(\sqrt{x^2-6x+9}-\sqrt{4x^2+4x+1}=0\)
Tìm GTNN:
A=\(\sqrt{25-10x+x^2}-\sqrt{x^2-6x+9}\)
B:\(\dfrac{1}{2x^2-x+3}\)
C: x2 - 2xy + 3y2 - 2x + 2017
D: x-\(\sqrt{x-2015}\)
E:\(\dfrac{2x+1}{x^2}\)
F: \(\dfrac{5x^2-4x+4}{x^2}\)
G=(x+1)(x+2)2(x+3)
H= X2-5x+y2+xy-4y+2014
I= x2 +xy +y2-3x-3y +2002
K=\(\sqrt{x^2-6x+2y^2+4y+11}+\sqrt{x^2+2x+3y^2+6y+4}\)
BT1: Rút gọn:
A=\(\dfrac{3x}{x-2}\sqrt{4-4x+4}vớix>2\)
B=\(\dfrac{-5y}{x+3}\sqrt{x^2+6x+9}vớix\ne-3\)
giải phương trình
a)\(\sqrt{x^2-6x+9}=4\)
b)\(\sqrt{4x^2-4x+1}=5x+3\)
c)\(\sqrt{x^2-9}+\sqrt{x^2-6x+9}=0\)
d)\(\sqrt{x^2+2x+1}+\sqrt{x^2-4x+4}=3\)
e)\(\sqrt{9x^2-12x+4}=\sqrt{x^2-10x+25}\)
Rút gọn:
\(\sqrt{4+2\sqrt{3}}+\sqrt{4-2\sqrt{3}}-\frac{5}{\sqrt{3}-2\sqrt{2}}-\frac{5}{\sqrt{3}+\sqrt{8}}\)
Giải các phường trình sau:
1) \(\sqrt{2x-1}=\sqrt{5}\)
2) \(\sqrt{3}x^2-\sqrt{12}=0\)
3) \(\sqrt{x-5}=3\)
4) \(\sqrt{4x^2}-6\)
5) \(\sqrt{\left(x-3\right)^2}=9\)
6) \(\sqrt{4\left(1-x\right)^2}-6=0\)
7) \(\sqrt{9\left(x-1\right)}=21\)
8) \(\sqrt[3]{x+1}=2\)
9) \(\sqrt{4x^2+4x+1}=6\)
10) \(\sqrt{2}x-\sqrt{50}=0\)
11) \(\sqrt{\left(2x-1\right)^2}=3\)
12) \(\sqrt[3]{3-2x}=-2\)
Mọi người ơi giúp em với!!! :((((
Bài 3: Giari phương trình \(\sqrt{A}\)=B
a> \(\sqrt{3x-1}\)
b> \(\sqrt{-3x+4}\) = 12
c> \(\sqrt{x^2-8x+16}\) = 4
d> \(\sqrt{9\left(x-1\right)}\) = 21
g> \(\sqrt{2-3x}\) = 10
h> \(\sqrt{4x}\) = \(\sqrt{5}\)
i> \(\sqrt{4-5x}\) = 12
p> \(\sqrt{16x}\) = 8
q> \(\sqrt{\left(x-3\right)^2}\) = 3
v> \(\sqrt{\dfrac{-6}{1+x}}\) = 5
w> \(\sqrt{4x-20}-3\)\(\sqrt{\dfrac{x-5}{9}}\) = \(\sqrt{1-x}\)
x> \(\sqrt{4x+8}\) + 2\(\sqrt{x+2}\) - \(\sqrt{9x+18}\) = 1
a'> \(\sqrt{x^2-6x+9}\)+x=11
z> \(\sqrt{16\left(x+1\right)^2}\) - \(\sqrt{9\left(x+1\right)}\) = 4
b'> \(\sqrt{9x+9}\) + \(\sqrt{4x+4}\) = \(\sqrt{x+1}\)
