Question

Find the roots of x+1/x= 3. ​

Answer 1

Answer:

Step-by-step explanation:

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

Step-by-step explanation:

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

To find : The roots of the given expression?

Solution :

We write the given expression in simpler form,

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

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

x^2+1=3x

x^2-3x+1=0 is the quadratic equation.

Using quadratic formula,

General form - ax^2+bx+c=0 D=b^2-4ac  

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

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

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

D=b^2-4ac

D=(-3)^2-4(1)(1)

D=9-4

D=5

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

x=\frac{-(-3)\pm\sqrt{5}}{2(1)}  

x=\frac{3\pm\sqrt{5}}{2}  

Therefore, The roots areGeneral form - ax^2+bx+c=0 D=b^2-4ac  

Answer 2

Step-by-step explanation:

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