Question

1. Show that x square - xy + y square is a rational number When x=√2-1÷√2+1 and y=√2+1÷√2-1​

Answer 1

Answer:

x=

2

−1

2

+1

=(

2

−1

2

+1

)×

2

+1

2

+1

=

2−1

(

2

+1)

2

∴x=

3+2

2

y=

2

+1

2

−1

=

2

+1

2

−1

×

2

−1

2

−1

=

2−1

(

(2−1)

2

)

∴y=

3−2

2

∴xy=(3+2

2

)

2

+(3−2

2

)

∴

xy

=9−8=

1

Now x

2

+y

2

=(3+2

2

)

2

+(3−2

2

)

2

=9+8+12

2

+9+8−12

2

∴

x

2

+y

2

=34

∴x

2

+y

2

+xy=34+1=35

∴x

2

+y

2

+xy=35

Answer 2

Refer to the attachment.

Hope it helps uh !