\(\sqrt{x+5}=\sqrt{x}+1\)
\(\Leftrightarrow x+5=\left(\sqrt{x}+1\right)^2\)
\(\Leftrightarrow x+5=x+2\sqrt{x}+1\)
\(\Leftrightarrow x+5-x-2\sqrt{x}-1=0\)
\(\Leftrightarrow4-2\sqrt{x}=0\)
\(\Leftrightarrow2\left(2-\sqrt{x}\right)=0\)
\(\Leftrightarrow2-\sqrt{x}=0\)
\(\Leftrightarrow\sqrt{x}=2\)
\(\Leftrightarrow x=4\)
Giải phương trình
\(\frac{3\left(x-\sqrt{3}\right)\left(x-\sqrt{5}\right)}{\left(1-\sqrt{3}\right)\left(1-\sqrt{5}\right)}+\frac{4\left(x-1\right)\left(x-\sqrt{5}\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}-\sqrt{5}\right)}+\frac{5\left(x-1\right)\left(x+\sqrt{3}\right)}{\left(\sqrt{5}-1\right)\left(\sqrt{5}-\sqrt{3}\right)}=3x-2\)
tìm x:
\(\sqrt{x^2+x+1}=1\)
\(\sqrt{x^2+1}=-3\)
\(\sqrt{x^2-10x+25}=7-2x\)
\(\sqrt{2x+5}=5\)
\(\sqrt{x^2-4x+4}-2x+5=0\)
\(\left(\dfrac{x-5\sqrt{x}}{x-25}-1\right):\left(\dfrac{25-x}{x+2\sqrt{x}-15}-\dfrac{\sqrt{x}+3}{\sqrt{x}+5}+\dfrac{\sqrt{x}-5}{\sqrt{x}-3}\right)\)
Bài toán :
Giải phương trình :
\(\frac{3.\left(x-\sqrt{3}\right)\left(x-\sqrt{5}\right)}{\left(1-\sqrt{3}\right)\left(1-\sqrt{5}\right)}+\frac{4\left(x-1\right)\left(x-\sqrt{5}\right)}{\left(\sqrt{3}-1\right)\left(\sqrt{3}-5\right)}+\frac{5\left(x-1\right)\left(x-\sqrt{3}\right)}{\left(\sqrt{5}-1\right)\left(\sqrt{5}-\sqrt{3}\right)}=3x-2\)
\(P=\dfrac{\sqrt{x}-1}{\sqrt{x}+1}-\dfrac{\sqrt{x}+3}{\sqrt{x}-2}-\dfrac{x+5}{x-\sqrt{x}-2}\)
\(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8+6\sqrt{x-1}}=5\)
\(x^{2^{ }}+\sqrt{x+5}=5\)
Giải phương trình:
*\(\sqrt{x^2-4x+5}+\sqrt{x^2-4x+8}+\sqrt{x^2-4x+9}=3+\sqrt{5}\)
*\(\sqrt{x+3-4\sqrt{x-1}+\sqrt{x+8+6\sqrt{x-1}=5}}\)
Tìm ĐKXĐ
\(\dfrac{\sqrt{x^2-5}}{x}\) ; \(\sqrt{\dfrac{x-1}{x+12}}\) ; \(\sqrt{6-x}\) ; \(\sqrt{x^2-16}\) ; \(\sqrt{-x^2+x-1}\)
Giải phương trình:
a) \(2\sqrt{x}\) + 1 = \(\sqrt{2}\) = 5
b) \(\dfrac{\sqrt{x-1}}{\sqrt{x-2}}\)= \(\dfrac{1}{2}\)
c) \(\dfrac{1}{\sqrt{x-3}}\) = \(\dfrac{2}{\sqrt{x-5}}\)
a. \(\sqrt{x}\left(\sqrt{x}-3\right)-5\left(\sqrt{x}+3\right)\)
b. \(3\left(2+\sqrt{x}\right)+\left(\sqrt{x}+3\right)\left(2-\sqrt{x}\right)\)
c. \(\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)-5\left(\sqrt{x}-1\right)\)
d. \(3\left(\sqrt{x}-2\right)-\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)
