Question

if x=root 5 + 2 / root 5 + 2 , find x + 1 / x

Answer 1

Dear student if the data you given is right, then

X = 1 {since x = (√5+2)/(√5+2) = 1 }
And x+(1/x) will be 2.

But I think that data was a little wrong.

I think your required x is

x = (√5-2)/(√5+2)
{Taking conjugate of denominator (i.e.√5-2) and multiplying it with both numerator and denominator}
x = (√5-2)²/(√5²-2²)
= (5-4√5+4)/1
= 9-4√5
1/x = 1/(9-4√5)
{Taking conjugate of denominator (i.e.,9+4√5) and multiplying it with both numerator and denominator}
= 9+4√5/(9²-(4√5)²)
= 9+4√5/1
​​​​​​ = 9+4√5

So x+(1/x) = 9-4√5 + 9+4√5
= 18

Dear student I've done this question on the assumption that x = √5-2/√5+2
If the right value of x is √5+2/√5-2, kindly do it by your self by the same method I've done here.
I can't do that also since you haven't mentioned the question correctly. So kindly do it by your self and kindly award point to this section.