Question

if a ³+1/a ³=18√3, prove that a²=5+2√6

Answer 1

Given p=2−a

to prove a3+6ap+p3−8=0...(1)

Now put the value of P in eq (1)

a3+6a(2−a)+(2−a)3−8=0

⇒a3+12a−6a2+8−a3−12a+6a2−8=0

[∴(a−b)3=a3−b3−3a2b+3ab2]

⇒0=0 (By eliminating equal terms we 

have LHS = RHS)