A positive number plus it's reciprocal is twice the original number. What is the number?

Question

written in algerebic form. 

Answer 1

Hi Devaughn,

 

 A positive number plus it's reciprocal is twice the original number. What is the number?

 

The reciprocal of a number x is 1/x

 

Let x= the positive number

The reciprocal =1/x

 

x +1/x=2x     Multiply the entire equation by x

 

x[x +1/x=2x ]   Distribute the x

 

x·x+x·1/x= x·2x   simplify

 

x²+1=2x^{2     subtract x2 from both sides}

 

1=x²    Take the square root of both sides

 

√1=√x²    When a square root is forced, the response is ±

 

±1=x     

 

There are two answers but the question asked for the POSITIVE value

which is x=1

 

 

ANSWER:  x=1

 

hope thsi helps you...