a.\(\sqrt{5x^2+14x+9}=5\sqrt{x+1}+\sqrt{x^2-8x-20}\)
b.\(\left(x+1\right)\left(x-3\right)+3\sqrt{x^2-x-3}=4\)
c. \(\sqrt{4x^2+x-1}=x+1\)
cứu với mọi ng ơi ☘
Giải hệ PT: \(\left\{{}\begin{matrix}x+\sqrt{\left(x+1\right)y}=2y-1\\\sqrt{2x+3}+\sqrt{y}=x^2-y\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\left(\sqrt{4x^2+3}-2x\right)\left(\sqrt{y^2-2y+4}-y+1\right)=3\\\sqrt{4x^2+2y+2}-\sqrt{3x+y}=2x+1\end{matrix}\right.\)
giải hệ pt
Giải hệ phương trình :
\(\left\{{}\begin{matrix}\sqrt{3+2x^2y-x^4y^2}+x^4\left(1-2x^2\right)=y^2\\1+\sqrt{1+\left(x-y\right)^2}=x^3\left(x^3-x+2y^2\right)\end{matrix}\right.\)
\(\left\{{}\begin{matrix}2y^3+y+2x\sqrt{1-x}=3\sqrt{1-x}\\y+\sqrt{2y^2+1}=4\sqrt{x+4}\end{matrix}\right.\)
Giải hpt:
\(\left\{{}\begin{matrix}\sqrt{x^2+3}+2\sqrt{x}=3+\sqrt{y}\\\sqrt{y^2+3}+2\sqrt{y}=3+\sqrt{x}\end{matrix}\right.\)
Giải hệ phương trình \(\left\{{}\begin{matrix}\left(x^2+y^2\right)\left(x+y\right)=x+y-2xy\\x^2+11x+6=2\sqrt{9y-5}+\sqrt{x+y}\end{matrix}\right.\)
+) Giải hệ pt: \(\left\{{}\begin{matrix}4\sqrt{x^2+4y-5}=y^2-x+10\\x^3+\left(1-y\right)x^2=\left(x+4\right)y\end{matrix}\right.\)
+) Cho a,b,c>0 và a+b+c=2017
CM: \(\dfrac{2017a-a^2}{bc}+\dfrac{2017b-b^2}{ca}+\dfrac{2017c-c^2}{ab}\ge\sqrt{2}\left(\Sigma\sqrt{\dfrac{2017-a}{a}}\right)\)
\(\left\{{}\begin{matrix}\sqrt{x+y}=2+\sqrt{x-y}\\\sqrt{x^2+y^2+1}-\sqrt{x^2-y^2}=3\end{matrix}\right.\)