If x -3-2 then the value of x -1- x is rational or irrational

Yes x 1/x will be irrational. x=3+√(2) 1/x=1/3+√(2) = 3 √(2)/(3+√(2))(3 √(2))=3 √(2)/9 2=3 √(2)/7 ∴ x 1/x=3+√(2) 3 √(2)/7=21+7√(2) 3+√(2)/7 =18+8√(2)/7 ...

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Standard IX

Mathematics

Rationalising Surds

If x =3+√2 th...

Question

If $x = 3 + \sqrt{2}$ then the value of $x - \frac{1}{x}$ is rational or irrational

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Solution

Yes $x - \frac{1}{x}$ will be irrational.
$x = 3 + \sqrt{2}$
$\frac{1}{x} = \frac{1}{3 + \sqrt{2}} = \frac{3 - \sqrt{2}}{(3 + \sqrt{2}) (3 - \sqrt{2})} = \frac{3 - \sqrt{2}}{9 - 2} = \frac{3 - \sqrt{2}}{7}$
$∴ x - \frac{1}{x} = 3 + \sqrt{2} - \frac{3 - \sqrt{2}}{7} = \frac{21 + 7 \sqrt{2} - 3 + \sqrt{2}}{7}$
$= \frac{18 + 8 \sqrt{2}}{7}$

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Similar questions

Q. STATEMENT-1 : If

f (x) = {\begin{matrix} x, & i f x i s r a t i o n a l 1 - x, & i f x i s i r r a t i o n a l \end{matrix}

, then

{lim}_{x \to 1 / 2}

f(x) does not exist.
STATEMENT-2 :

x \to 1 / 2

can be a rational or an irrational value.

Q. If

x = 3 + 2 \sqrt{2}

, then find whether

x + \frac{1}{x}

is rational or irrational.

Q. Statement

I :

f (x) = {\begin{matrix} x, & if x is rational 1 - x, & if x is irrational \end{matrix},

then

lim x \to 1 / 2 f (x)

does not exist.

Statement

I I :

x \to \frac{1}{2}

can be a rational or an irrational value

Q. If

x = 3 + 2 \sqrt{2}

, check whether

x + \frac{1}{x}

is rational or irrational.

f (x) = {\begin{matrix} x^{2} i f x i s i r r a t i o n a l 1 i f x i s r a t i o n a l \end{matrix}

, then

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If x=3+√2 then the value of x−1x is rational or irrational

Yes x−1x will be irrational. x=3+√2 1x=13+√2=3−√2(3+√2)(3−√2)=3−√29−2=3−√27 ∴x−1x=3+√2−3−√27=21+7√2−3+√27 =18+8√27

If $x = 3 + \sqrt{2}$ then the value of $x - \frac{1}{x}$ is rational or irrational