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Find the product of all real values of r for which 1/(2x) = (r - x)/5 has exactly one real solution.

 Jul 23, 2022
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1/ (2x)  = (r  - x)  / 5

 

5  =  2x ( r - x)

 

5 =  2rx- 2x^2

 

2x^2 - 2rx + 5

 

If this has one  real solution  then  the discriminant =  0   .....so.....

 

(-2r)^2 - 4 (2) ( 5) = 0

 

4r^2  -  40  =  0

 

4r^2=   40

 

r^2  =  10

 

r = sqrt (10)      or    r  =  -sqrt (10)

 

Their product =   -10

 

 

cool cool cool

 Jul 23, 2022

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