Question

If a - 1/a = 10 ; find: a + 1/a , a ^ 2 - 1/(a ^ 2)​

Answer 1

Step-by-step explanation:

a-\frac{1}{a}=\pm 4a−

a

1

=±4

Step-by-step explanation:

Given : a^2+\frac{1}{a^2}=18a

2

+

a

2

1

=18

To find : The value of a-\frac{1}{a}a−

a

1

?

Solution :

Using identity,

(x-y)^2=x^2+y^2-2xy(x−y)

2

=x

2

+y

2

−2xy

Let x=ax=a and y=\frac{1}{a}y=

a

1

Substitute in the identity,

(a-\frac{1}{a})^2=a^2+\frac{1}{a^2}-2\times a\times \frac{1}{a}(a−

a

1

)

2

=a

2

+

a

2

1

−2×a×

a

1

(a-\frac{1}{a})^2=18-2(a−

a

1

)

2

=18−2

(a-\frac{1}{a})^2=16(a−

a

1

)

2

=16

Taking root both side,

a-\frac{1}{a}=\pm 4a−

a

1