Question

If a+1/a=6 and a ¥0;find:a^2-1/a^2​

Answer 1

Answer:

a−

a

1

=8

Squaring both sides,

=(a−

a

1

)

2

=8

2

=a

2

+(

a

1

)

2

−2(a)(

a

1

)=64

=a

2

+

a

2

1

−2=64

=a

2

+

a

2

1

=66

Now,

(a+

a

1

)

2

=a

2

+

a

2

1

+2(a)(

a

1

)

=66+2

=68

=>a+

a

1

=

68

=±2

1

7

Now,

a

2

−

a

2

1

=(a+

a

1

)(a−

a

1

)

=±(2

1

7)(8)

=±16

1

7