Expert: Sherman D. - 9/17/2004

Question
-------------------------
Followup To
Question -
 
 (1/rootx + rootx ) ^2

Can you please explain the above equation.

The answer in the book is  1/x + x + 2.  I cannot work out the answer. i know that 1/Root x = x^-1/2
and rootx = x^1/2
Answer -
so if by this you mean

((1/(sqrt(x))) + sqrt(x))^2

Multiply the inside by sqrt(x), and you get

((1 + x)/(sqrt(x)))^2

Now square it

((1 + x)^2)/(sqrt(x)^2)

((1 + x)(1 + x))/x

(1 + x + x + x^2)/x

(1 + 2x + x^2)/x

or you can say

(1/x) + 2 + x

or as your book has it

(1/x) + x + 2
It is not squared x but root of x in the question.

Answer
don't know if you know this, but when i put

((1/(sqrt(x))) + sqrt(x))^2

where as (1/(sqrt(x))) + sqrt(x) is the ONLY thing being square.

sqrt(x) is the short way to saying SQuare RooT

just like

cbrt = CuBed RooT

the rest after that are mostly typed as

4thrt
5thrt
6thrt
etc...

if i wanted to say "x" squared, i would had just typed it as

((1/(x^2)) + x^2)^2

if you noticed when i showed that sqrt(x)^2 cancelled out leaving you with "x" instead of x^4

Let me do it this way

((1/(sqrt(x))) + sqrt(x))^2

Multiply everything by sqrt(x) to cancel out the fractions

((1/(sqrt(x))) * sqrt(x)) + (sqrt(x) * sqrt(x)))
((sqrt(x))/(sqrt(x))) + (sqrt(x))^2)
1 + x

This has to be all over sqrt(x) to get it all as one fraction

(1 + x)/(sqrt(x))

Don't forget that (1 + x) and sqrt(x) both have to be squared

((1 + x)(1 + x))/(((sqrt(x)))^2)
Use the FOIL Method
(1 + x + x + x^2)/x

(1 + 2x + x^2)/x

becomes

(1/x) + ((2x)/x) + ((x^2)/x)

becomes

(1/x) + 2 + x

this is the same as saying (1/x) + x + 2