Question

Giải phương trình :

a) \(\left(\sqrt{x}-2\right)\left(5-\sqrt{x}\right)=4-x\)

b) \(\frac{\sqrt{x+5}}{\sqrt{x+4}}=\frac{\sqrt{x-2}}{\sqrt{x+3}}\)

c) \(\frac{1}{x+\sqrt{x^2+1}}+\frac{1}{x-\sqrt{x^2+1}}=4\)

Answer 1

a, ĐKXĐ: \(x\ge0\)

\(pt\Leftrightarrow5\sqrt{x}-10-x+2\sqrt{x}=4-x\)

\(\Leftrightarrow7\sqrt{x}=14\)

\(\Leftrightarrow x=4\left(tm\right)\)

\(\Rightarrow\) phương trình có nghiệm \(x=4\)

b, ĐKXĐ: \(x\ge2\)

\(pt\Leftrightarrow\frac{x+5}{x+4}=\frac{x-2}{x+3}\)

\(\Leftrightarrow\left(x+5\right)\left(x+3\right)=\left(x+4\right)\left(x-2\right)\)

\(\Leftrightarrow x^2+8x+15=x^2+2x-8\)

\(\Leftrightarrow x=-\frac{23}{6}\left(l\right)\)

\(\Rightarrow\) vô nghiệm

c, ĐKXĐ: \(x\in R\)

\(pt\Leftrightarrow\frac{x-\sqrt{x^2+1}+x+\sqrt{x^2+1}}{\left(x+\sqrt{x^2+1}\right)\left(x-\sqrt{x^2+1}\right)}=4\)

\(\Leftrightarrow-2x=4\)

\(\Leftrightarrow x=-2\left(tm\right)\)

\(\Rightarrow\) phương trinh có nghiệm \(x=-2\)