Question

if (a²+1/a²) =27 , find the value of (i) (a-1/a) (ii) (a³-1/a³)​

Answer 1

Answer:

a

2

+

a

2

1

=18

(a−

a

1

)

2

=a

2

+

a

2

1

−2

⇒(a−

a

1

)

2

=18−2

⇒(a−

a

1

)

2

=16

⇒(a−

a

1

)=±

16

⇒(a−

a

1

)=±4......(1)

(a−

a

1

)

3

=a

3

−

a

3

1

−3×a×

a

1

(a−

a

1

)

⇒a

3

−

a

3

1

=(a−

a

1

)

3

+3(a−

a

1

)

⇒a

3

−

a

3

1

=(±4)

3

+3(±4) [From (1)]

⇒a

3

−

a

3

1

=±76