Question

If x = root5-2 and y = root5+2 ; find (i) x square (ii) y square (iii) xy (iv) x square + y square + xy

Answer 1

Answer:

Correct option is

A

323

We rationalize the denominator,

x=

5

+2

5

−2

×

5

−2

5

−2

x=

5−4

5+4−3

5

x=

1

9−4

5

.

Then, x

2

=(9−4

5

)(9−4

5

)

=81+16×5−72

5

=161−72

5

.

We rationalize the denominator,

y=

5

−2

5

+2

×

5

+2

5

+2

y=

5−4

5+4+4

5

y=

1

9+4

5

.

Then, y

2

=(9+4

5

)(9+4

5

)

=81+16×5+72

5

=161+72

5

.

Now, x=

5

−2

5

+2

and y=

5

+2

5

−2

.

Then, xy=

5

−2

5

+2

×

5

+2

5

−2

xy=1 .

Therefore, x

2

+y

2

+xy=161−72

5

+161+72

5

+1=323.