Question

anwer this image please

Answer 1

a=7-4root3

let square root of 7-4root3 = rootx-rooty

squaring both the side we get

7-4root3=x+y-2rootxy

so

x+y=7

2rootxy=4root3

rootxy=2root3

again squaring both the side we get

xy=12

(x+y)^2=x^2+y^2+2xy

49=x^2+y^2+24

x^2+y^2=25

(x-y)^2=x^2+y^2-2xy

(x-y)^2=25-24

(x-y)^2=1

(x-y)=1

by adding equations 1&2 we get

2x=8

x=4

y=3

square root of 7-4root3 = 2-root3

so roota+1/roota

=2-root3+1/2-root3

=2-root3+2 +root3

=4

so your answer is 4