Verified answer

Answer:

√5 + 2

Step-by-step explanation:

To solve the given expression, let's break it down step by step:

√5 + 2 / 1√5 - 2 X √5 - 2 / √5 - 2

First, let's simplify the expression inside the parentheses:

√5 - 2

Next, let's simplify the division:

√5 + 2 / 1√5 - 2 X (√5 - 2) / (√5 - 2)

Since the numerator and denominator of the division are the same, they cancel out:

√5 + 2 X 1

Now, let's simplify the multiplication:

√5 + 2

Therefore, the simplified form of the given expression is:

√5 + 2

Step-by-step explanation:

Correct option is A)

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.