please, can someone help me with this algebra problem....?

Question

i have a big test on this tomorrow that i need to do well on. here's the question:

what is the conjugate of the reciprocal of 2 (radical) 5 - 3 (radical) 2?

thanks to whoever can help

Answer 1

the reciprocal would be 1/(2 (rad) 5 - 3 (rad) 2)

The Conjugate of that expression that you are probably looking for is
(2 (rad) 5 + 3 (rad) 2)/(2 (rad) 5 + 3 (rad) 2)
which is what you multiply the reciprocal by to rationalize the denominator which means you are taking
1/(2 (rad) 5 - 3 (rad) 2) * (2 (rad) 5 + 3 (rad) 2) / (2 (rad) 5 + 3 (rad) 2)

As a result you get

(2 (rad) 5 + 3 (rad) 2) / 2

Answer 2

The recriprocal means 1 over the value so it is 1/(2 sqrt(5)-3sqrt(2)). The conjugate means that we change the sign between the two expressions.

So the conjugate is 2 sqrt(5)+3sqrt(2).

Answer 3

x=2!!!

Thanks for the points!