Tìm x,y,z biết: x+y+z+35 = \(2\left(2\sqrt{x+1}+3\sqrt{y+2}+4\sqrt{z+3}\right)\)
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Tìm x,y,z biết
\(x+y+z+35=2\left(2\sqrt{x+1}+3\sqrt{y+2}+4\sqrt{z+3}\right)\)
\(x+y+z+35=2\left(2\sqrt{x+1}+3\sqrt{y+2}+4\sqrt{z+3}\right)\)
\(\Leftrightarrow x+y+z+35-4\sqrt{x+1}-6\sqrt{y+2}-8\sqrt{z+3}=0\)
\(\Leftrightarrow\left(x+1-4\sqrt{x+1}+4\right)+\left(y+2-6\sqrt{y+2}+9\right)+\left(z+3-8\sqrt{z+3}+16\right)=0\)
\(\Leftrightarrow\left(\sqrt{x+1}-2\right)^2+\left(\sqrt{y+2}-3\right)^2+\left(\sqrt{z+3}-4\right)^2=0\)
\(\Leftrightarrow\hept{\begin{cases}\left(\sqrt{x+1}-2\right)^2=0\\\left(\sqrt{y+2}-3\right)^2=0\\\left(\sqrt{z+3}-4\right)^2=0\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}\sqrt{x+1}=2\\\sqrt{y+2}=3\\\sqrt{z+3}=4\end{cases}}\)
\(\Leftrightarrow\hept{\begin{cases}x=3\\y=7\\z=13\end{cases}}\)
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Tìm các số x, y, z biết
\(x+y+z+35=2\left(2\sqrt{x+1}+3\sqrt{y+2}+4\sqrt{z+3}\right)\)
\(x+y+z+35=2\left(2\sqrt{x+1}+3\sqrt{y+2}+4\sqrt{z+3}\right)\)
b) \(x^2+8x-3=2\sqrt{x\left(8+x\right)}\)
c)\(\sqrt{x-2}+\sqrt{x+1}+\sqrt{2x+3}=6\)
Tìm x,y,z biết:
x+y+z+35 = \(2.\left(2\sqrt{x+1}+3\sqrt{y+2}+4\sqrt{z+3}\right)\)
ĐKXĐ: ....
\(x+1-4\sqrt{x+1}+4+y+2-6\sqrt{y+2}+9+z+3-8\sqrt{z+3}+16=0\)
\(\Leftrightarrow\left(\sqrt{x+1}-2\right)^2+\left(\sqrt{y+2}-3\right)^2+\left(\sqrt{z+3}-4\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x+1}=2\\\sqrt{y+2}=3\\\sqrt{z+3}=4\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=3\\y=7\\z=13\end{matrix}\right.\)
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tìm x,y,z biết câu a \(x+y+z+8=2\sqrt{x-1}+4\sqrt{y-2}+6\sqrt{z-3}\) câu b \(x+y+4=2\sqrt{x}+4\sqrt{y-1}\) câu c \(x+y+z=2\left(2\sqrt{x+1}+3\sqrt{y+2}+4\sqrt{z+3}\right)+35\)
tìm x,y,z biết
x+y+z+35=\(2\left(2\sqrt{x+1}+3\sqrt{y+2}+4\sqrt{z+3}\right)\)
ĐKXĐ: \(\left\{{}\begin{matrix}x\ge-1\\y\ge-2\\z\ge-3\end{matrix}\right.\)
x+y+z+35=\(4\sqrt{x+1}+6\sqrt{y+2}+8\sqrt{z+3}\)
\(\Leftrightarrow\left(x+1-2.2\sqrt{x+1}+4\right)+\left(y+2-2.3\sqrt{y+2}+9\right)+\left(z+3-2.4\sqrt{z+3}+16\right)=0\)
\(\Leftrightarrow\left(\sqrt{x+1}-2\right)^2+\left(\sqrt{y+2}-3\right)^2+\left(\sqrt{z+3}-4\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(\sqrt{x+1}-2\right)^2=0\\\left(\sqrt{y+2}-3^{ }\right)^2=0\\\left(\sqrt{z+3}-4\right)^2=0\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=7\\z=13\end{matrix}\right.\)
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Cho \(x+y+z+35=2\left(2\sqrt{x+1}+3\sqrt{y+2}+4\sqrt{z+3}\right)\)Vậy x=...;y...;z=...
chả cần HĐT dùng Cosi cx đc
\(\left(x+1\right)+4\ge4\sqrt{x+1}\)
\(\left(y+2\right)+9\ge6\sqrt{y+2}\)
\(\left(z+3\right)+16\ge8\sqrt{z+3}\)
\(\Rightarrow VT\ge VP\).Dấu = khi x=3;y=7;z=13
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cho biết \(x+y+z+35=2\left(2\sqrt{x+1}+3\sqrt{y+2}+4\sqrt{z+3}\right)\)
\(\Leftrightarrow x+y+z+35=4\sqrt{x+1}+6\sqrt{y+2}+8\sqrt{z+3}\)
\(\Leftrightarrow x+1-4\sqrt{x+1}+4+y+2-6\sqrt{y+2}+9+z+3-8\sqrt{z+3}+16=0\)
\(\Leftrightarrow\left(\sqrt{x+1}-2\right)^2+\left(\sqrt{y+2}-3\right)^2+\left(\sqrt{z+3}-4\right)^2=0\)
cho từng cái ngoặc bằng 0 thì ta được x=3 ; y=7 ;z=13 nếu đúng tick nha bạn
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Tìm x,y,z biết:
a.\(\sqrt{x}+\sqrt{y-1}+\sqrt{z-2}=\dfrac{1}{2}\left(x+y+z\right)\)
b.\(\sqrt{x-2}+\sqrt{y+1995}+\sqrt{z-1996}=\dfrac{1}{2}\left(x+y+z\right)\)