Question

If x = 2 + √3, then the value of (x + 1/x) is?

Answer 1

the value would be 3

Answer 2

so x+1/x=4

Explanation:

x=2+√3

for 1/x we take reciprocal of x

1/x=1/2+√3

first we will rationalize 1/x

multiplying and dividing by 2-√3

1/x=1/2+√3 × 2-√3/2-√3

1/x=2-√3/(2+√3)(2-√3)

as we know that (a-b)(a+b)=a²+b²

1/x=2-√3/(2)²-(√3)²

1/x=2-√3/4-3

1/x=2-√3

now x+1/x

x+1/x=2+√3+2-√3

2+2+√3-√3

x+1/x=4

i hope it will help you