Question

Please answer the question asap.

Answer 1

10

Explanation:

First we can let
`u=x^(2)` --> this simplifies the question to
`u+(1)/(u)`.

We can find u by solving for x squared.

Using
`(a+b)^2=a^2+2ab+b^2` we can find
`x^2=(\sqrt3+\sqrt2)^2=3+2\sqrt6+2=5+2\sqrt6`.

Now since we have u, we can plug into the equation to solve for the answer.

`5+2\sqrt6+(1)/(5+2\sqrt6)`

We can rationalize the denominator of the fraction by multiplying by the conjugate:
`(1)/(5+2\sqrt6)\cdot(5-2\sqrt6)/(5-2\sqrt6) =(5-2\sqrt6)/(25-24)=(5-2\sqrt6)/(1)`.

Now add the terms together:
`5+2\sqrt6+5-2\sqrt6=10`