Ta có pt \(\Leftrightarrow\sqrt{x^2+4\sqrt{x^2-4}}=16-2x^2\Leftrightarrow\sqrt{x^2-4+4\sqrt{x^2-4}+4}=16-2x^2\Leftrightarrow\sqrt{\left(\sqrt{x^2-4}+2\right)^2}=16-2x^2\)
\(\Leftrightarrow\sqrt{x^2-4}+2=16-2x^2\Leftrightarrow\sqrt{x^2-4}=14-2x^2\Leftrightarrow\sqrt{a-4}=14-2a\)( với a=x^2)
đến đây bn tự giải pt bậc 2 nhá
1) Rút gọn biểu thức
P=\(\left(\dfrac{x+2\sqrt{x}+4}{x\sqrt{x}-8}+\dfrac{x+2\sqrt{x}+4}{x-1}\right):\left(3+\dfrac{1}{\sqrt{x}-2}+\dfrac{2}{\sqrt{x}+1}\right)\)
giải pt :
a) \(\sqrt{x-1}+\sqrt{x^3+x^2+x+1}=1+\sqrt{x^4-1}\)
b0 \(4\sqrt{x+1}=x^2-5x+14\)
c) \(2x+3\sqrt{4-5x}+\sqrt{x+2}=8\)
d) \(\dfrac{x^2+x}{\sqrt{x^2+x+1}}=\dfrac{2-x}{\sqrt{x-1}}\)
\(A=\dfrac{8-x}{2+\sqrt[3]{x}}:\left(2+\dfrac{\sqrt[3]{x^2}}{2+\sqrt[3]{x}}\right)+\left(\sqrt[3]{x}+\dfrac{2\sqrt[3]{x}}{\sqrt[3]{x}-2}\right)\dfrac{\sqrt[3]{x^2}-4}{\sqrt[3]{x^2}+2\sqrt[3]{x}}\)
Rút gọn các biểu thức
a, \(A=\dfrac{\sqrt{3}-\sqrt{6}}{1-\sqrt{2}}-\dfrac{2+\sqrt{8}}{1+\sqrt{2}}\)
b, \(B=\left(\dfrac{1}{x-4}-\dfrac{1}{x+4\sqrt{x}+4}\right).\dfrac{x+2\sqrt{x}}{\sqrt{x}}\) (với x >0, x ≠ 4)
\(1,x=\sqrt{3-x}.\sqrt{4-x}+\sqrt{4-x}.\sqrt{5-x}+\sqrt{5-x}.\sqrt{3-x}\)
2) \(\dfrac{x^2-4}{x}+\dfrac{y^2-4}{y}+8=4\left(\sqrt{x-1}+\sqrt{y-1}\right)\)
rút gọn biểu thức sau
a.\(\sqrt{8}-\sqrt{18}+2\sqrt{32}\)
b.\(\left(\dfrac{1}{\sqrt{x}+4}+\dfrac{1}{\sqrt{x}-4}\right)\dfrac{\sqrt{x}+4}{\sqrt{x}}\) với x>0,x\(\ne16\)
gpt:
\(a,\sqrt{2x+4}-2\sqrt{2-x}=\dfrac{6x-4}{\sqrt{x^2+4}}\)
b) \(\sqrt{\dfrac{6}{3-x}}+\sqrt{\dfrac{8}{2-x}}=6\)
\(\left(\dfrac{x+2\sqrt{x}+4}{x\sqrt{x}-8}+\dfrac{x+2\sqrt{x}+1}{x-1}\right)\): \(\left(\dfrac{3\sqrt{x}-5}{\sqrt{x}-2}+\dfrac{2\sqrt{x}+10}{x+6\sqrt{x}+5}\right)\)
\(\dfrac{\sqrt{x+2-4\sqrt{x-2}}+\sqrt{x+2+4\sqrt{x-2}}}{\sqrt{\dfrac{4}{x^2}}-\dfrac{4}{x}+1}\)
Giải phương trình:
1. \(\sqrt{2x^2+4x+7}=x^4+4x^3+3x^2-2x-7\)
2. \(\dfrac{4}{x}+\sqrt{x-\dfrac{1}{x}}=x+\sqrt{2x-\dfrac{5}{x}}\)
3. \(\dfrac{6-2x}{\sqrt{5-x}}+\dfrac{6+2x}{\sqrt{5+x}}=\dfrac{8}{3}\)
4. \(x^2+1-\left(x+1\right)\sqrt{x^2-2x+3}=0\)
5. \(2\sqrt{2x+4}+4\sqrt{2-x}=\sqrt{9x^2+16}\)
6. \(\left(2x+7\right)\sqrt{2x+7}=x^2+9x+7\)
