If a + 1/a = ? 3, then the value of a⁶ - 1/a⁶ + 2 will be

Given equation is,
a + 1/a = ?3 .............................(i)
On squaring both sides
? a² + 1/a² + 2 = 3
? a² + 1/a² = 1 ..............................(ii)

Now, multiplying Equation (i) and (ii), we get
(a + 1/a) (a² + 1/a²) = ?3
? a³ + a/a² + a²/a + 1/a³ = ?3
? a³ + 1/a³ + ( a + 1/a ) = ?3
now put the value of a + 1/a in above equation,
? a³ + 1/a³ + ?3 = ?3 [from Eq. (i)]
? a³ + 1/a³ = 0
? ( a⁶ + 1 ) /a³ = 0
? a⁶ + 1 = 0 x a³
? a⁶ + 1 = 0
? a⁶ = -1
? a⁶ - 1/a⁶ + 2
put the value of a⁶
= (-1)⁶ - 1/(-1)⁶ + 2
= 1 - 1 + 2 = 2