Question

Giải phương trình

1) \(\left(x-2\sqrt{x}+4\right)\left(x+3\sqrt{x}+4\right)=14x\)

2)\(\left(x+2\sqrt{x}+2\right)\left(x+4\sqrt{x}+2\right)=4\sqrt{x}+4\)

3)\(2x^4+3x^3+x^2+6x+8=0\)

Answer 1

1: \(\Leftrightarrow\left(x+4\right)^2+\sqrt{x}-6x-14x=0\)

\(\Leftrightarrow\left(x+4\right)^2+\sqrt{x}-20x=0\)

\(\Leftrightarrow\left(x+4+5\sqrt{x}\right)\left(x+4-4\sqrt{x}\right)=0\)

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

=>x=4

2: \(\Leftrightarrow\left(x+2\right)^2+6\sqrt{x}+8x-4\sqrt{x}-4=0\)

\(\Leftrightarrow\left(x+2\right)^2+2\sqrt{x}+8x-4=0\)

\(\Leftrightarrow x^2+4x+4+2\sqrt{x}+8x-4=0\)

\(\Leftrightarrow x^2+12x+2\sqrt{x}=0\)

=>x=0