\(=\lim\limits_{x\rightarrow+\infty}\left(\sqrt{x^2+2x}-\sqrt{x^2+x}+x-\sqrt{x^2+x}\right)\)
\(=\lim\limits_{x\rightarrow+\infty}\left(\dfrac{x}{\sqrt{x^2+2x}+\sqrt{x^2+x}}-\dfrac{x}{x+\sqrt{x^2+x}}\right)\)
\(=\lim\limits_{x\rightarrow+\infty}\left(\dfrac{1}{\sqrt{1+\dfrac{2}{x}}+\sqrt{1+\dfrac{1}{x}}}-\dfrac{1}{1+\sqrt{1+\dfrac{1}{x}}}\right)=\dfrac{1}{2}-\dfrac{1}{2}=0\)
giải pt :
a, \(\left(2x-6\right)\sqrt{x+4}-\left(x-5\right)\sqrt{2x+3}=3\left(x-1\right)\)
b, \(\left(4x+1\right)\sqrt{x+2}-\left(4x-1\right)\sqrt{x-2}=21\)
c, \(\left(4x+2\right)\sqrt{x+1}-\left(4x-2\right)\sqrt{x-1}=9\)
d, \(\left(2x-4\right)\sqrt{3x-2}+\sqrt{x+3}=5x-7+\sqrt{3x^2+7x-6}\)
giải pt :
a, \(\sqrt{x-\sqrt{x^2-1}}+\sqrt{x+\sqrt{x^2-1}}=2\)
b, \(\left(x^2+2\right)^2+4\left(x+1\right)^3+\sqrt{x^2+2x+5}=\left(2x-1\right)^2+2\)
c, \(\sqrt{4x^2+x+6}=4x-2+7\sqrt{x+1}\)
d, \(\sqrt{x-2}-\sqrt{x+2}=2\sqrt{x^2-4}-2x+2\)
giải pt :
a, \(\left(x^2+2\right)^2+4\left(x+1\right)^3+\sqrt{x^2+2x+5}=\left(2x-1\right)^2+2\)
b, \(\sqrt{4x^2+x+6}=4x-2+7\sqrt{x+1}\)
c, \(\sqrt{x-2}-\sqrt{x+2}=2\sqrt{x^2-4}-2x+2\)
giải pt :a,\(\left(2x+6\right)\sqrt{x+4}-\left(x-5\right)\sqrt{2x+3}=3\left(x-1\right)\)
b, \(\left(4x+1\right)\sqrt{x+2}-\left(4x-1\right)\sqrt{x-2}=21\)
c, \(\left(4x+2\right)\sqrt{x+1}-\left(4x-2\right)\sqrt{x-1}=9\)
d, \(\left(2x-4\right)\sqrt{3x-2}+\sqrt{x+3}=5x-7+\sqrt{3x^2+7x-6}\)
giải phương trình :
a, \(\sqrt{x+1}+x+3=\sqrt{1-x}+3\sqrt{1-x^2}\)
b,\(\left(2x-3\right)\sqrt{3+x}+2x\sqrt{3-x}=6x-8+\sqrt{9-x^2}\)
c, \(2x^2-5x+22=5\sqrt{x^3-11x +20}\)
d, \(x^3-3x^2+2\sqrt{\left(x+2\right)^3}=6x\)
giaỉ pt:
a, \(\sqrt{x +1}+2\left(x+1\right)=x-1+\sqrt{1-x}+3\sqrt{1-x^2}\)
b, \(14\sqrt{x+35}+6\sqrt{x+1}=84+\sqrt{x^2+36x+35}\)
c, \(x\sqrt{2x+3}+3\left(\sqrt{x+5}+1\right)=3x+\sqrt{2x^2+13x+15}+\sqrt{2x+3}\)
giải pt :
a, \(\dfrac{\sqrt{x-3}}{\sqrt{2x-1}-1}=\dfrac{1}{\sqrt{x+3}-\sqrt{x-3}}\)
b, \(\left(\sqrt{x^2+x+1}+\sqrt{4x^2+x+1}\right)\left(\sqrt{5x^2+1}-\sqrt{2x^2+1}\right)=3x^2\)
giải phương trình :
a, \(\left(x+1\right)\sqrt{x+8}=x^2+x+4\)
b, \(\left(2x+7\right)\sqrt{2x+7}=x^2+9x+7\)
c, \(\left(3x+1\right)\sqrt{x^2+3}=3x^2+2x+3\)
giải pt :
a,\(2x^2-11x+21=3\sqrt[3]{4x-4}\)
b,\(\dfrac{\sqrt{x-3}}{\sqrt{2x-1}-1}=\dfrac{1}{\sqrt{x+3}-\sqrt{x-3}}\)
c,\(\left(\sqrt{x^2+x+1}+\sqrt{4x^2+x+1}\right)\left(\sqrt{5x^2+1}-\sqrt{2x^2+1}\right)=3x^2\)
