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)