Question

If a + 1/a = 6, find a^3 + 1/a^3

Answer 1

your answer:-

given:-

a+1/a=6

to find a3+1/a3

solution:-

using formula:-

(a+1/a)3=a3+1/a3 +3×a×1/a(a+1/a)

it's just like the formula of (a+b)3=a3+b3+3ab(a+b)

now putting values

(6)3=a3+1/a3+3(6)

216=a3+1/a3+18

216-18=a3+1/a3

198=a3+1/a3

thanks

@ananya☺

Answer 2

GOOD MORNING!!!

a + 1/a = 6 { Given }

a³ + 1/a³ = { a + 1/a }³ - 3 { a + 1/ a }

=>

a³ + 1/a³ = { 6 }³ - 3 { 6 }

=>

a³ + 1/a³ = 216 - 18

=>

a³ + 1/a³ = 198

______________________________

a³ + 1/a³ = ( a + 1/a ) ³ - 3 ( a + 1/a )

proof:-

R.H.S

a³ + 1/a³ + 3a²/a + 3a/a² - 3a - 3/a

=>

a³ + 1/a³ + 3a + 3/a - 3a - 3/a

=>

a³ + 1/a³ Hence, proved