Question

lf x=3-2√2 then find out the value of x+1/x​

Answer 1

Given:

• x =3-2√2

To Find:

• The value of x +1/x .

Concept Used:

• We will first find 1/x .
• Then we will rationalise the denominator.

Solution:

Given that x =3-2√2.

So,

$\sf{\implies x=3-2\sqrt{2}}$

$\sf{\implies \dfrac{1}{x}=\dfrac{1}{3-2\sqrt{2}}}$

$\sf{\implies \dfrac{1}{x}=\dfrac{1(3+2\sqrt{2})}{(3+2\sqrt{2})(3-2\sqrt{2})}}$

$\sf{\implies \dfrac{1}{x}=\dfrac{3+2\sqrt{2}}{(3)^{2}-(2\sqrt{2})^{2}}}$

using

• (a+b)(a-b)=a²-b².

$\sf{\implies \dfrac{1}{x}=\dfrac{3+2\sqrt{2}}{9-8}}$

${\underline{\boxed{\red{\sf{\leadsto\dfrac{1}{x}=3+2\sqrt{2}}}}}}$

Now , x + 1/x

=$\sf{3+2\sqrt{2}+3-2\sqrt{2}}$

=${\underline{\red{\sf{9}}}}$

Hence the required answer is 9.