Bình phương 2 vế , ta được :
\(\left(x^2+x-1\right)^2=\left(x^2+4x+4\right)\left(x^2-2x+2\right)\)
\(\Leftrightarrow x^4+x^2+1+2x^3-2x^2-2x=x^4+4x^3+4x^2-2x^3-8x^2-8x+2x^2+8x+8\)
\(\Leftrightarrow x^4+2x^3-x^2-2x+1=x^4+2x^3-2x^2+8\)
\(\Leftrightarrow x^2-2x-7=0\)
\(\Leftrightarrow\left(x-1\right)^2=8\)
\(\Leftrightarrow x=\pm\sqrt{8}+1\)
Vậy ...
Giải PT: \(\sqrt{\left(x^2+2x\right)^2+4\left(x+1\right)^2}-\sqrt{x^2+\left(x+1\right)^2+\left(x^2+x\right)^2}=2019\)
Giải PT: \(\sqrt{x-1}+\sqrt{x+3}+2\sqrt{\left(x-1\right).\left(x^2-3x+5\right)}=4-2x\)
1\(\left\{{}\begin{matrix}xy\left(x+y\right)=2\\x^3+y^3+x^3y^3+7\left(x+1\right)\left(y+1\right)=31\end{matrix}\right.\)
2 giải pt \(9+3\sqrt{x\left(3-2x\right)}=7\sqrt{x}+5\sqrt{3-2x}\)
Giải PT: \(\sqrt{x+5}+\sqrt{3-x}-2.\left(\sqrt{15-2x-x^2}+1\right)=0\)
Giải PT: \(\left(x+1\right).\sqrt{2x^2-2x}=2x^2-3x-2\)
giải pt: a) \(\sqrt{x+1}+\sqrt{5x}=\sqrt{4x-3}+\sqrt{2x+4}\)
b) \(\left(x-1\right)\left(x+2\right)+2\sqrt[]{x^2+x+1}=0\)
Giải pt:
\(2\left(1-x\right)\sqrt{x^2+2x-1}=x^2-2x-1\)
Giải pt:
\(x^2\left(x^2+2\right)=4-x\sqrt{2x^2+4}\)
giải pt:
1,\(\sqrt{x+\dfrac{3}{x}}=\dfrac{x^2+7}{2\left(x+1\right)}\)
2, \(\left(x+3\right)\sqrt{\left(4-x\right)\left(12+x\right)}=28-x\)
3, \(\sqrt{x^3-x}=2x^2-x-2\)
Giải pt:
\(x^3+\left(x+1\right)\sqrt{x+1}+2\sqrt{2}=\left(x+\sqrt{x+1}+\sqrt{2}\right)^3\)
