proove a -√x = 1/(a + √x )

Question

Surd based problm in genral

 

I had got 6 -√35 =   1/(1+√35

Answer 1

a-√x=1/(a+√x) is true when a=√(x+1)

 

(a-√x)(a+√x)=1

a²-x=1

a²=x+1

√a²=√(x+1)

a=√(x+1)

in other words, it is true when x is 1 less than the square of a

Answer 2

6-√35 = (6-√35)(6+√35)/(6+√35) = 1/(6+√35)

 

However, a-√x is not always the same as 1/(a+√x).

 

For example, 7-√35 = 14/(7+√35)

Answer 3

a - √x = ?

 

Multiply and divide by a + √x

 

a - √x = (a - √x)(a + √x)/(a + √x) = (a² - x)/(a + √x) ≠ 1/(a + √x)

 

It looks like there is an error in the problem statement.