# If x = 3 + √8 , find the value of x^2 + 1/x^2.

By BYJU'S Exam Prep

Updated on: September 25th, 2023

Given: x = 3 + √8 (equation 1)

To find: the the value of x2 + 1/x2

Let us find the value of 1/x using the vale given in equation 1:

x = 3 + √8

then, 1/x = 1/(3 + √8) (equation 2)

Now, we have to rationalize the denominator of the value obtained in equation 2.

So, for rationalization we will multiply the numerator and denominator of 1/(3 + √8) with (3 – √8).

1/x = 1 x (3 – √8) / (3 + √8) x (3 – √8)

1/x = (3 – √8) / (3)2 + 3√8 – 3√8 – (√8)2

1/x = (3 – √8) / (3)2 – (√8)2

1/x = (3 – √8) / (9 – 8)

1/x = (3 – √8) / 1

1/x = (3 – √8)

Now, we have the value of x = (3 + √8) and the value of 1/x = (3 – √8)

So, the value of x2 + 1/x2 = (3 + √8)2 + (3 – √8)2 (equation 3)

Apply (a+b)2 and (a-b)2 formula in (equation 3)

x2 + 1/x2 = (3)2 + (√8)2 + 2 x 3 x √8 + (3)2 + (√8)2 – 2 x 3 x √8

x2 + 1/x2 = (3)2 + (√8)2 + (3)2 + (√8)2

x2 + 1/x2 = 9 + 8 + 9 + 8

x2 + 1/x2 = 34

Hence, the value of x2 + 1/x2 for x = 3 + √8 is 34.

Table of content

## Value of x2 + 1/x2 if x = 3 + √8

As discussed above, the value of x2 + 1/x2 is 34. It can be obtained easily by rationalizing the denominator of x = 3 + √8. So, candidates must be aware of the steps of rationalization in order to solve these types of problems.

In elementary algebra, the process of rationalization is used to get rid of the irrational number in the denominator. To rationalize the denominator, a variety of techniques are available. Making something more effective is the literal meaning of the word rationalize.

• Its use in mathematics entails simplifying and reducing the equation to its more useful form.
• An algebraic fraction’s denominator can be reduced by a process known as rationalization, which involves removing radicals.
• To put it another way, eliminate the radicals from a fraction so that the denominator is only a rational number.

Summary:

## If x = 3 + √8 , find the value of x2 + 1/x2.

For x = 3 + √8, the value of x+ 1/x2 is 34To find the value, the concept of rationalization is to be used wherein find the value of 1/x which is 1 / (3 + √8) and then multiply the numerator and denominator of 1 / (3 + √8) with (3 – √8). After that, solve the equation to get the answer.

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