SOLUTION: What's an example of an equation containing two radicals for where 1 is a solution?

We want an equation of this form



That's "something + something = something"

Let's make up a simple addition or subtraction example 
as a model like this simple addition example:

                          3 + 4 = 7

We want  to equal 3 when x=1
We want  to equal 4 when x=1
We want  to equal 7 when x=1

Let's create an expression1:

Squaring both sides:


Start with x = 1
Multiply through by something, say 4
          4x = 4
Add enough to both sides to make the right side come out to 9.
So we add 5 to both sides
        4x+5 = 9

So 4x+5 will do for expression1

Let's create an expression2:

Squaring both sides:


Start with x = 1
Multiply through by something, say 5
          5x = 5
Add enough to both sides to make the right side come out to 16.
So we add 11 to both sides
        5x+11 = 5+11
        5x+11 = 16

So 5x+11 will do for expression2

Let's create an expression3:
It's not a radical. We want it to equal 7 when 1
is substituted for x

Start with x = 1
Multiply through by something, say 8
          8x = 8
Subtract enough from both sides to make the right side come out to 7.
So we subtract 1 from both sides
        8x-1 = 8-1
        8x-1 = 7

So 8x-1 will do for expression3




becomes this equation



Edwin