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ধরি, \(\cfrac{x}{lm-n^2}=\cfrac{y}{mn-l^2}=\cfrac{z}{nl-m^2}=k \) (যেখানে \(k≠0\))
\(∴x=k(lm-n^2 ),y=k(mn-l^2 ) \) এবং \(z=k(nl-m^2 ) \)

\(lx+my+nz\)
\(=l×k(lm-n^2 )+m×k(mn-l^2 )
+n× k(nl-m^2 )\)
\(=k(l^2 m-n^2 l+m^2 n-l^2 m+n^2 l-m^2 n)\)
\(=k×0\)
\(=0\) (প্রমানিত)