Question

If x = 7 - 4√3 , find the value of x + 1 /x

Answer 1

Answer:

answer for the given problem is

Answer 2

Answer:

Answer is 4

Step-by-step explanation:

Given : x = 7- 4√3, therefore, 1/x = 1/(7- 4√3)

Given : x = 7- 4√3, therefore, 1/x = 1/(7- 4√3)=> 1/x = 1* (7+ 4√3)/(7- 4√3)*(7+ 4√3)

Given : x = 7- 4√3, therefore, 1/x = 1/(7- 4√3)=> 1/x = 1* (7+ 4√3)/(7- 4√3)*(7+ 4√3)=> 1/x = (7+ 4√3)/(7² - 4² * 3)

Given : x = 7- 4√3, therefore, 1/x = 1/(7- 4√3)=> 1/x = 1* (7+ 4√3)/(7- 4√3)*(7+ 4√3)=> 1/x = (7+ 4√3)/(7² - 4² * 3)=> 1/x = (7+ 4√3)/(49 - 48)

Given : x = 7- 4√3, therefore, 1/x = 1/(7- 4√3)=> 1/x = 1* (7+ 4√3)/(7- 4√3)*(7+ 4√3)=> 1/x = (7+ 4√3)/(7² - 4² * 3)=> 1/x = (7+ 4√3)/(49 - 48)=> 1/x = (7+ 4√3)

=> x + 1/x = 7- 4√3 + 7+ 4√3

=> x + 1/x = 7- 4√3 + 7+ 4√3=> x + 1/x = 14 - - - - (i)

Now, (√x + 1/√x )² = x + 1/x + 2* √x * 1/√x

Now, (√x + 1/√x )² = x + 1/x + 2* √x * 1/√x=> (√x + 1/√x )² = x + 1/x + 2

Now, (√x + 1/√x )² = x + 1/x + 2* √x * 1/√x=> (√x + 1/√x )² = x + 1/x + 2=> (√x + 1/√x )² = 14 + 2

Now, (√x + 1/√x )² = x + 1/x + 2* √x * 1/√x=> (√x + 1/√x )² = x + 1/x + 2=> (√x + 1/√x )² = 14 + 2=> (√x + 1/√x ) = √16 - - {considering only positive value}

Now, (√x + 1/√x )² = x + 1/x + 2* √x * 1/√x=> (√x + 1/√x )² = x + 1/x + 2=> (√x + 1/√x )² = 14 + 2=> (√x + 1/√x ) = √16 - - {considering only positive value}=> √x + 1/√x = 4 ==> (Ans)