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\(\left(x^3-\cfrac{1}{y^3}\right)\propto \left(x^3+\cfrac{1}{y^3}\right)\)
বা, \(\left(x^3-\cfrac{1}{y^3}\right)=k\cdot \left(x^3+\cfrac{1}{y^3}\right)\) [\(k\) অশূন্য ভেদ ধ্রুবক]
বা, \(x^3-\cfrac{1}{y^3}=kx^3+\cfrac{k}{y^3}\)
বা, \(x^3-kx^3=\cfrac{1}{y^3}+\cfrac{k}{y^3}\)
বা, \(x^3(1-k)=\cfrac{1}{y^3}(1+k)\)
বা, \(x^3y^3=\cfrac{(1+k)}{(1-k)}\)
বা, \((xy)^3=\cfrac{(1+k)}{(1-k)}\)
বা, \(xy=\sqrt[3]{\cfrac{(1+k)}{(1-k)}}=\) ধ্রুবক
\(\therefore x\propto \cfrac{1}{y}\) [প্রমাণিত]