Question

Giải các phương trình sau:

a) \(x\sqrt{x-1}+\left(2x+1\right)\sqrt{x+2}+x^3-4x^2+x-6=0\)

b) \(\left(2x+3\right)\sqrt{2x-1}+x\sqrt{x+3}+x^2-5x-3=0\)

c) \(x\sqrt{2x+3}+\left(x+1\right)\sqrt{4x-1}+2\left(x^2-x-1\right)=0\)

Answer 1

a) ĐKXĐ: \(x\ge1\).

\(PT\Leftrightarrow x\left(\sqrt{x-1}-1\right)+\left(2x+1\right)\left(\sqrt{x+2}-2\right)+\left(x^3-4x^2+6x-4\right)=0\)

\(\Leftrightarrow\left(x-2\right)\left(\frac{x}{\sqrt{x-1}+1}+\frac{2x+1}{\sqrt{x+2}+2}+x^2-2x+2\right)=0\)

\(\Leftrightarrow x=2\left(TMĐK\right)\)

Answer 2

b) Cách làm cũng giống như thế :v

ĐKXĐ: \(x\ge\frac{1}{2}\)

\(PT\Leftrightarrow\left(x-1\right)\left(\frac{4x+6}{\sqrt{2x-1}+1}+\frac{x}{\sqrt{x+3}+2}+x\right)=0\)

\(\Leftrightarrow x=1\) (TMĐK)