Question

If a-1/a=3,evaluate a²+1/a² and a⁴+1/a⁴​

Answer 1

Step-by-step explanation:

It is given that,

a

2

−1/a

2

=5

So,

By using the formula, (a+b)

2

[a

2

−1/a

2

]

2

=a

4

+1/a

4

−2

[a

2

−1/a

2

]

2

+2=a

4

+1/a

4

Substitute the value of a

2

−1/a

2

=5, we get

5

2

+2=a

4

+1/a

4

a

4

+1/a

4

=25+2

=27

Answer 2

Step-by-step explanation:

a-1/3=a

a-1=3a

2a=-1

a=-1/2

a²=1/4

a⁴=1/16

a²+1/a²=1/4+4=17/4

a⁴+1/a⁴=1/16+16=257/16