Question

If (x+1/x)=4, find the value of (x²+1/x²)​

Answer 1

Answer:

x

2

+

x

2

1

=14

Step-by-step explanation:

We have,

x+\dfrac{1}{x}=4x+

x

1

=4 .....(1)

To find, x^2+\dfrac{1}{x^2}=?x

2

+

x

2

1

=?

Squaring (1) in both sides, we get

(x+\dfrac{1}{x})^{2}=4^{2}(x+

x

1

)

2

=4

2

⇒ x^2+\dfrac{1}{x^2}+2.x.\dfrac{1}{x} =16x

2

+

x

2

1

+2.x.

x

1

=16

⇒ x^2+\dfrac{1}{x^2}+2 =16x

2

+

x

2

1

+2=16

⇒x^2+\dfrac{1}{x^2}=16-2=14x

2

+

x

2

1

=16−2=14

∴ x^2+\dfrac{1}{x^2}=14x

2

+

x

2

1

=14

Hence, x^2+\dfrac{1}{x^2}=14x

2

+

x

2

1

=14

Answer 2

Answer:

so long the answer is ok