Question

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

Answer 1

Explanation:

x=7+4√3. (1)

x+1/x=7+4√3+ 1/7+4√3

rationalize the term of 1/x

1/x=> 7-4√3/1. = >7-4√3. (2)

solve the of given question

x+1/x=>> 7+4√3+7-4√3. ( using eqs. (1) & (2)

x+1/x=14

Answer 2

Answer:14

Explanation:

Provided x=7+4√3

{ x+1/x <=> [(x^2)+1]÷x }

x^2=(7+4√3)^2=49+48+56√3 { from the equation-->(a+b)^2=a^2+b^2+2ab }

(x^2) +1=48+49+56√3 +1=98+56√3

[(x^2)+1]÷x=[98+56√3]÷[7+(4√3)]

Consider, 98+56√3=14*(7+(4√3))

Hence,we may conclude [98+56√3]÷[7+(4√3)]=14*(7+(4√3))÷(7+(4√3))=14*(1÷1)=14