a: \(P=\dfrac{\left(\sqrt{x^2+1}\right)^2+5\sqrt{x^2+1}+6}{\sqrt{x^2+1}+3}+\dfrac{\left(\sqrt{x^2+1}^2\right)+7\sqrt{x^2+1}+12}{\sqrt{x^2+1}+4}\)
\(=\sqrt{x^2+1}+2+\sqrt{x^2+1}+3\)
\(=2\sqrt{x^2+1}+5\)
b: Để P=11 thì \(2\sqrt{x^2+1}=11-5=6\)
=>căn (x^2+1)=3
=>x^2+1=9
=>x^2=8
=>\(x=\pm2\sqrt{2}\)
Cho P = \(\left(\dfrac{1}{\sqrt{x}+1}-\dfrac{2\sqrt{x}-2}{x\sqrt{x}-\sqrt{x}+x-1}\right)\): \(\left(\dfrac{1}{\sqrt{x}-1}+\dfrac{2}{x-1}\right)\)
a/ Tim DKXD va rut gon P
b/ Tim cac gia tri nguyen cua x de P co gia tri nguyen
Rut gon P=\(\dfrac{3x+6\sqrt{x}}{x+\sqrt{x}-2}-\dfrac{\sqrt{x-1}}{\sqrt{x}+2}+\dfrac{\sqrt{x}+2}{1-\sqrt{x}}\)
Tim x de P dat gia tri lon nhat
Cho \(A=\dfrac{\sqrt{x-1-2\sqrt{x-2}}}{\sqrt{x-1}-1}\)
a/Tim DKXD cua A
b/Rut gon A
Cho A = \(\frac{3\sqrt{x}-3}{x\sqrt{x}-2x+2\sqrt{x}-1}-\frac{4x\sqrt{x}-4}{x^3-1}\)(x>1). Rut gon A va tim x de A=1
Rut gon A= \(\dfrac{\sqrt{1-\sqrt{1-x^2}}.\left\{\sqrt{\left(x+1\right)^3}+\sqrt{\left(1-x\right)^3}\right\}}{2-\sqrt{1-x^2}}\)
cho \(P=\left(\dfrac{\sqrt{x}-1}{3\sqrt{x}-1}-\dfrac{1}{3\sqrt{x}+1}+\dfrac{8\sqrt{x}}{9x-1}\right)\div\left(1-\dfrac{3\sqrt{x}-2}{3\sqrt{x}+1}\right)\)
1, rút gọn P
2, tìm x để \(P\ge0\)
tính P khi \(x=-\sqrt{3-2\sqrt{2}}+\dfrac{\sqrt{7+\sqrt{5}}+\sqrt{7-\sqrt{5}}}{\sqrt{7+2\sqrt{11}}}\)
\(A=\frac{\sqrt{x}+4}{\sqrt{x}+2};B=\left(\frac{\sqrt{x}}{\sqrt{x}+4}+\frac{4}{\sqrt{x}-4}\right):\frac{x+16}{\sqrt{x}+2}\)
a. rut gon B
b. Tim x nguyen de P = B(A-1) nguyen
giup minh voi a
Bài 1 . Tính giá trị các biểu thức sau :
a) √11-4√7 + \(\dfrac{2\sqrt{7}-2}{\sqrt{7}-1}\) b) \(\left(\sqrt{125}-3\sqrt{3}\right).\dfrac{\sqrt{5}+\sqrt{3}}{8+\sqrt{15}}\)
Bài 2 . Cho biểu thức : A=\(\dfrac{2}{\sqrt{x}-1}+\dfrac{1}{\sqrt{x}+3}+\dfrac{5-x}{\left(1-\sqrt{x}\right)\left(\sqrt{x}+3\right)}\)với x>0 , x \(\ne\)1
a) Rút gọn A
b) Giả sử A = \(\sqrt{2}\) . Chứng tỏ rằng : \(\sqrt{x}-\sqrt{2}\) là số nguyên
Giải các phương trình sau:
1. \(\sqrt{x^2-\dfrac{1}{4}+\sqrt{x^2+x+\dfrac{1}{4}}}=\dfrac{1}{2}\left(2x^3+x^2+2x+1\right)\)
2. \(x^2+4x+7=\left(x+4\right)\sqrt{x^2+7}\)
3. \(\sqrt{x-1}+\sqrt{x^3+x^2+x+1}=1+\sqrt{x^4-1}\)
4. \(\sqrt{x^2-3x+2}+\sqrt{x+3}=\sqrt{x-2}+\sqrt{x^2+2x-3}\)
5. \(x=\left(\sqrt{x}+2\right)\left(1-\sqrt{1-\sqrt{x}}\right)\)
6. \(2\sqrt[3]{2x-1}=x^3+1\)
7. \(\sqrt{x-\dfrac{1}{x}}+\sqrt{1-\dfrac{1}{x}}=x\)
