Question

lf x - 3 = 1/x , find the value of x²+1/x² answer ​

Answer 1

Answer:

5

Step-by-step explanation:

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Answer 2

Answer:

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}}⟹x=3−2

2

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

x

1

=

3−2

2

1

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

x

1

=

(3+2

2

)(3−2

2

)

1(3+2

2

)

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

x

1

=

(3)

2

−(2

2

)

2

3+2

2

using

(a+b)(a-b)=a²-b².

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

x

1

=

9−8

3+2

2

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

⇝

x

1

=3+2

2

Now , x + 1/x

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

2

+3−2

2

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

9

Hence the required answer is 9.