ai giúp mình với ạ
\(\left(3x+4y+5z\right)^2=50\left(x^2+y^2+z^2\right)\)
\(\Leftrightarrow9x^2+16y^2+25z^2+24xy+40yz+30zx=50\left(x^2+y^2+z^2\right)\)
\(\Leftrightarrow41x^2+34y^2+25z^2-24xy-40yz-30zx=0\)
\(\Leftrightarrow\left(16x^2-24xy+9y^2\right)+\left(25y^2-40yz+16z^2\right)+\left(9z^2-30zx+25x^2\right)=0\)
\(\Leftrightarrow\left(4x-3y\right)^2+\left(5y-4z\right)^2+\left(3z-5x\right)^2=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(4x-3y\right)^2=0\\\left(5y-4z\right)^2=0\\\left(3z-5x\right)^2=0\end{matrix}\right.\Leftrightarrow\dfrac{x}{3}=\dfrac{y}{4}=\dfrac{z}{5}\left(đpcm\right)\)
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