Question

x = over root 7+4root3 find the value x+1/x.

Answer 1

since

x=√(7+4√3),

we can write it as

x=√[4+3+2×2×√3],

then

x=√[(2)²+(√3)²+2×2×√3],


x=√(2+√3)²,


then

x=(2+√3),


then

1/x=(2-√3),


therefore

x+1/x =(2+√3)+(2-√3),


x+1/x=2+√3+2-√3,


x+1/x=4