Question

Giải phương trình vô tỉ :

\(\sqrt{x}-\sqrt{x-1}-\sqrt{x-4}+\sqrt{x+9}=0\)

Answer 1

\(\\\Leftrightarrow \sqrt{x}+\sqrt{x+9}=\sqrt{x-1}+\sqrt{x-4} \\\Leftrightarrow \left ( \sqrt{x}+\sqrt{x+9} \right )^{2}=\left ( \sqrt{x-1}+\sqrt{x-4} \right )^{2} \\\Leftrightarrow 2x+9+2\sqrt{x(x+9)}=2x-5+2\sqrt{(x-1)(x-4)} \\\Leftrightarrow 14+2\sqrt{x(x+9)}=2\sqrt{(x-1)(x-4)} \\\Leftrightarrow 7+\sqrt{x(x+9)}=\sqrt{(x-1)(x-4)} \\\Leftrightarrow 49+14\sqrt{x(x+9)}+x^{2}+9x=x^{2}-5x+4 \\\Leftrightarrow 14\sqrt{x(x+9)}=-14x-53\)

Answer 2

quên đk :v

ĐK: \(x\ge4\)