lf x - 3 = 1/x , find the value of x²+1/x² answer
Answers
Answer:
5
Step-by-step explanation:
hope u got it
have a great day ahead
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.