If $straight x equals 3 plus 2 square root of 2 comma$ check whether $straight x plus 1 over straight x$ is rational or irrational.

Solution

$x equals 3 plus 2 square root of 2 space space space space space space space space space space space space space space space space space.... left parenthesis 1 right parenthesis$
$1 over straight x equals fraction numerator 1 over denominator 3 plus 2 square root of 2 end fraction$
$equals fraction numerator 1 over denominator 3 plus 2 square root of 2 end fraction cross times fraction numerator 3 minus 2 square root of 2 over denominator 3 minus 2 square root of 2 end fraction equals fraction numerator 3 minus 2 square root of 2 over denominator left parenthesis 3 right parenthesis squared minus left parenthesis 2 square root of 2 right parenthesis squared end fraction equals space fraction numerator 3 minus 2 square root of 2 over denominator 9 minus 8 end fraction equals fraction numerator 3 minus 2 square root of 2 over denominator 1 end fraction equals space 3 minus 2 square root of 2 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space.... left parenthesis 2 right parenthesis$

Adding (1) and (2), we get

straight x plus 1 over straight x equals left parenthesis 3 plus 2 square root of 2 right parenthesis plus left parenthesis 3 minus 2 square root of 2 right parenthesis equals 6

For Daily Free Study Material Join wiredfaculty

Polynomials

If $straight x equals 3 plus 2 square root of 2 comma$ check whether $straight x plus 1 over straight x$ is rational or irrational.

Some More Questions From Polynomials Chapter

Find two rational numbers between 0.1 and 0.2.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction