Question

Find (√5+2)-(2√5-2) ​

Answer 1

Answer:

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.

Step-by-step explanation:

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Answer 2

(√5 ×2√5 )+(√5×2)-(2×2√5/)-(2×2)

10+2√5-4√5-4

6+2√5 -4√5