Question

if x=7+4root3 then find the value of x +1/x​

Answer 1

Answer:

Hey there, here's your answer.

Given:

x=7+4√3---(1)

therefore, 1/x= 1/(7+4√3)

Now, rationalize

1/x=1/(7+4√3)*(7-4√3)/(7-4√3)

or,1/x=(7-4√3)(1)

or,1/x=7-4√3----(2)

Adding equations (1) and (2), we get

x+ 1/x=(7+4√3)+(7-4√3)

or, x+ 1/x=(7+7)+(4√3- 4√3)

or, x+ 1/x=14

Hence, 14 is our answer.