Math, asked by justin6238791470, 3 months ago

finds the roots of following x-1/x=3 , x is not equal to 0​

Answers

Answered by uttamwadkute
1

Answer:

x=3 ( given)

3-1=2

so answer in 2

but I am not sure

Answered by poonamchhonkar007
21

Answer:

The roots are x=\frac{3+\sqrt{5}}{2},\frac{3-\sqrt{5}}{2}x=

2

3+

5

,

2

3−

5

Step-by-step explanation:

Given : Expression x+\frac{1}{x}=3;x\neq 0x+

x

1

=3;x

=0

To find : The roots of the given expression?

Solution :

We write the given expression in simpler form,

x+\frac{1}{x}=3x+

x

1

=3

\frac{x^2+1}{x}=3

x

x

2

+1

=3

x^2+1=3xx

2

+1=3x

x^2-3x+1=0x

2

−3x+1=0 is the quadratic equation.

Using quadratic formula,

General form - ax^2+bx+c=0ax

2

+bx+c=0 D=b^2-4acD=b

2

−4ac

Solution is x=\frac{-b\pm\sqrt{D}}{2a}x=

2a

−b±

D

Equation is x^2-3x+1=0x

2

−3x+1=0

where, a=1 , b=-3, c=1

D=b^2-4acD=b

2

−4ac

D=(-3)^2-4(1)(1)D=(−3)

2

−4(1)(1)

D=9-4D=9−4

D=5D=5

Solution is x=\frac{-b\pm\sqrt{D}}{2a}x=

2a

−b±

D

x=\frac{-(-3)\pm\sqrt{5}}{2(1)}x=

2(1)

−(−3)±

5

x=\frac{3\pm\sqrt{5}}{2}x=

2

5

Therefore, The roots are x=\frac{3+\sqrt{5}}{2},\frac{3-\sqrt{5}}{2}x=

2

3+

5

,

2

3−

5

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