Question

factorise ; x²+1/x²-18​

Answer 1

or, (x+

x

1

)

2

−2.x.

x

1

=18

or, (x+

x

1

)

2

−2=18

or, (x+

x

1

)

2

=18+2=20

or, x+

x

1

=

20

.

Again (1) can be written as

(x−

x

1

)

2

+2.x.

x

1

=18

or, (x−

x

1

)

2

+2=18

or, (x−

x

1

)

2

=18−2=16

or, x−

x

1

=4.

∴ the sum of x+

x

1

and x−

x

1

=4+

20

.