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দেওয়া আছে, (x+1/x)^3=3^3 [ঘন করে পাই] x^3+1/x^3+3.x.1/x(x+1/x)=27 x^3+1/x^3+3.3=27 x^3+1/x^3=27-9 x^3+1/x^3=18। (প্রমানিত)

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দেওয়া আছে, x³+1/x³ = 18 Let, x+1/x = m x³+1/x³ = (x+1/x)³-3×x×(1/x)(x+1/x) Or, m³-3m= 18 m³-3m-18 = 0 Let, F(m) =m³-3m-18 F(3)=3³-3.3-18=0 (m-3),F(m) এর একটি উৎপাদক। Now, m³-3m-18 = 0 m³-3m²+3m²-9m+6m-18=0 m²(m-3)+3m(m-3)+6(m-3)=0 (m-3)(m²+3m+6)=0 অতএব,  m-3=0 m=3 x+1/x= 3(proved)

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