Solve the equation x = 2 × 1 x + 1

Question

Find a number that is exactly 1 more than 2 times its reciprocal. That is, solve the equation x = 2 × 1 x + 1.

Answer 1

x=1+2(1/x)

x=1+(2/x)

x^2=x+2

x^2-x-2=0

(x-2)(x+1)=0

x-2=0

x=2

x+1=0

x=-1

two solutions:2 and -1

Answer 2

x = 2 * 1/x + 1

multiply by 2

 

x = 2/x + 1

subtract the 1 from both sides

 

x - 1 = 2/x

Multiply x by both sides

 

x(x - 1) = 2

multiply the x

 

x² - x = 2

subtract the 2 from both sides

 

x² - x - 2 = 0

Factor

 

(x - 2)(x + 1) = 0

Solutions are 2 and -1

 

check

2 = 2 * 1/2 + 1

2 = 1 + 1

 

-1 = 2 * -1 + 1

-1 = -2 + 1