ĐKXĐ: \(x\ge-2\).
Đặt \(\sqrt{x+2}=a;\sqrt{x^2-2x+4}=b\left(a,b\ge0\right)\).
PT đã cho tương đương:
\(2ab=b^2-3a^2\Leftrightarrow\left(a+b\right)\left(b-3a\right)=0\Leftrightarrow b=3a\).
Khi đó \(\sqrt{x^2-2x+4}=3\sqrt{x+2}\Leftrightarrow x^2-2x+4=9x+18\Leftrightarrow x^2-11x-14=0\Leftrightarrow...\).
\(\sqrt[3]{x^3+5x^2}-1=\sqrt{\dfrac{5x^2-2}{6}}\)
Giải pt
giải pt \(x^2+\left(3-x\right)\sqrt{2x-1}=x\left(3\sqrt{2x^2-5x+2}-\sqrt{x-2}\right)\)
giải pt \(\sqrt{x-2}+\sqrt{4-x}+\sqrt{2x-5}=2x^2-5x\)
2) \(x^2+x+2=\sqrt{5x+5}+\sqrt{3x+2}\)
giải pt : \(3\sqrt{3x-2}+6\sqrt{x-1}=7x-10+4\sqrt{3x^2-5x+2}\)
Giải PT : \(\sqrt{3x+1}\) + \(\sqrt{5x+4}\) = \(3x^2\) - \(x\) + 3
Giải pt
\(\sqrt{x-2}+\sqrt{4-x}=2x^2-5x-1\)
giải pt
a) \(\sqrt[3]{x+6}+\sqrt{x-1}=x^2-1\)
b) \(\sqrt[3]{x-9}+2x^2+3x=\sqrt{5x-1}+1\)
c) \(\sqrt{3x+1}-\sqrt{6-x}+3x^2-14x-8=0\)
d) \(\sqrt{x+1}-2\sqrt{4-x}=\frac{5\left(x-3\right)}{\sqrt{2x^2+18}}\)
e) \(x^3+5x^2+6x=\left(x+2\right)\left(\sqrt{2x+2}+\sqrt{5-x}\right)\)
giải pt
a) \(\sqrt{x^2+2}+\sqrt{x^2+7}=\sqrt{x^2+x+3}+\sqrt{x^2+x+8}\)
b) \(\sqrt{7-x^2+x\sqrt{x+5}}=\sqrt{3-2x-x^2}\)
c) \(\sqrt{10x+1}+\sqrt{3x-5}=\sqrt{9x+4}+\sqrt{2x-2}\)
d) \(\sqrt{x+7}+\sqrt{4x+1}=\sqrt{5x+6}+2\sqrt{2x+3}\)
e) \(\sqrt{x+4+2\sqrt{x+3}}=x+4\)
giải pt
a) \(\sqrt{x^2+x+1}+\sqrt{3x^2+3x+2}=\sqrt{5x^2+5x-1}\)
b) \(\sqrt{x^2+x+4}+\sqrt{x^2+x+1}=\sqrt{2x^2+2x+9}\)
c) \(\sqrt{3x^2-5x+7}+\sqrt{3x^2-7x+2}=3\)
d) \(\sqrt{x^2+3x+2}=\sqrt{2x^2+9x+7}-\sqrt{x^2+6x+5}\)
