ĐKXĐ: \(x\ge-21\)
\(\left(x+\sqrt{x^2+9}\right)\left(\sqrt{x+21}-x\right)=9\)
\(\Leftrightarrow\left(\sqrt{x^2+9}-x\right)\left(\sqrt{x^2+9}+x\right)\left(\sqrt{x+21}-x\right)=9\left(\sqrt{x^2+9}-x\right)\)
\(\Leftrightarrow\sqrt{x+21}-x=\sqrt{x^2+9}-x\)
\(\Leftrightarrow\sqrt{x+21}=\sqrt{x^2+9}\)
\(\Leftrightarrow x+21=x^2+9\)
\(\Leftrightarrow x^2-x-12=0\)
\(\Leftrightarrow...\)
GPT \(\sqrt{x-1}+\sqrt{9-x}+2\sqrt{-x^2+10x-9}=12\)
GPT: √5x2+14x+9−√x^2−x−20−−−−−−−−−√=5√x+1
GPT : \(\sqrt{\sqrt{x}+1-2\sqrt[4]{x}}+\sqrt{\sqrt{x}+9-6\sqrt[4]{x}}=2\)
GPT : x4+x3-8x2-9x=9
GPT nghiệm nguyên:
\(x^2+y^2-2x+y=9\)
GPT:√5x2+14x+9−√x^2−x−20=5√x+1
GPT : \(\sqrt{x^2-x-1}+\sqrt{x^2-9x-9}=2x\)
gpt \(\sqrt{\frac{x}{3}-3}+\sqrt{7-\frac{x}{3}}=2x-7-\frac{x^2}{9}\)
GPT
a) \(\sqrt{x}+\sqrt{x+1}=\frac{1}{\sqrt{x}}\)
b) \(\frac{x+3+2\sqrt{x^2-9}}{2x-6+\sqrt{x^2-9}}=\sqrt{2}\)
GPT: x3 - 3x2 + 7x =(9-x)\(\sqrt{5-x}\) + 5
