Question

if a+1/a=6 and a is not equal to 0 find a²-1/a²​

Answer 1

Answer:

a+

a

1

=6

Squaring both sides,

=(a+

a

1

)

2

=6

2

=a

2

+(

a

1

)

2

+2(a)(

a

1

)=36

=a

2

+

a

2

1

+2=36

=a

2

+

a

2

1

=34

Now,

(a−

a

1

)

2

=a

2

+

a

2

1

−2(a)(

a

1

)

=34−2

=32

=>a−

a

1

=±

32

=±4

2

Now,

(a

2

−

a

2

1

)=(a+

a

1

)(a−

a

1

)

=6(±4

2

)

=±24

2

Answer 2

a+6/a=6

a+6=6a

5a=6

a=6/5

putting value of a in in the given equation.

a²-1/a²=(6/5)²-(5/6)²

=(36/25)-(25/36)

36²-25²/25×36

1296-625/900 =0.745