The product

The product of a number plus that number and its inverse is two and one-half. What is the inverse of this number

Correct result:

z =  0.5

Solution:

x+1/x=2.5  x2+1=2.5x  x2+1=2.5 x x22.5x+1=0  a=1;b=2.5;c=1 D=b24ac=2.52411=2.25 D>0  x1,2=b±D2a=2.5±2.252 x1,2=1.25±0.75 x1=2 x2=0.5   Factored form of the equation:  (x2)(x0.5)=0  z=1/x1=1/2=12=0.5x + 1/x=2.5 \ \\ \ \\ x^2 + 1=2.5*x \ \\ \ \\ x^2 + 1=2.5 \cdot \ x \ \\ x^2 -2.5x +1=0 \ \\ \ \\ a=1; b=-2.5; c=1 \ \\ D=b^2 - 4ac=2.5^2 - 4\cdot 1 \cdot 1=2.25 \ \\ D>0 \ \\ \ \\ x_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ 2.5 \pm \sqrt{ 2.25 } }{ 2 } \ \\ x_{1,2}=1.25 \pm 0.75 \ \\ x_{1}=2 \ \\ x_{2}=0.5 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (x -2) (x -0.5)=0 \ \\ \ \\ z=1/x_{1}=1/2=\dfrac{ 1 }{ 2 }=0.5

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