সমাধান করো: \(\cfrac{x}{3}+\cfrac{3}{x}=4\cfrac{1}{4}\) Madhyamik 2009 , 1988
\(\cfrac{x}{3}+\cfrac{3}{x}=4\cfrac{1}{4}\)
বা, \(\cfrac{x^2+9}{3x}=\cfrac{17}{4}\)
বা, \(4(x^2+9)=51x\)
বা, \(4x^2+36=51x\)
বা, \(4x^2-51x+36=0\)
বা, \(4x^2-(48+3)x+36=0\)
বা, \(4x^2-48x-3x+36=0\)
বা, \(4x(x-12)-3(x-12)=0\)
বা, \((x-12)(4x-3)=0\)
\(\therefore\) হয়, \((x-12)=0 \) অর্থাৎ, \(x=12\)
নয়, \((4x-3)=0\) বা, \(x=\cfrac{3}{4}\)
\(\therefore\) নির্ণেয় সমাধান \(x=12\) অথবা \(x=\cfrac{3}{4}\) (Answer)