- Home/
- CTET & State TET (Earlier - TEACHING)/
- General /
- Article
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 x2 + 1/x2 is 34. To 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.
Related Questions:
- Find Three Different Irrational Numbers Between 5/7 and 9/11.
- Give Some Examples of Each Monocot and Dicot Seed
- Express 0.99999…. in the form p/q
- The sum of two numbers is 8 and the sum of their reciprocals is 8/15. Find the numbers.
- A magnesium ribbon is burnt in oxygen to give a white compound X accompanied by the emission of light. If the burning ribbon is now placed in an atmosphere of nitrogen, it continues to burn and forms a compound Y. Write the chemical formulae of X and Y.
- When Lead Nitrate reacts with Potassium Iodide then a Yellow Precipitate of
- The Number of all Possible Matrices of Order 3 × 3 with Each Entry 0 to 1 is
