+0  
 
0
269
1
avatar

There are two distinct solutions $x$ to the equation $18+5x^2=20x$. If each solution is rounded to the nearest integer, and then these two integers are multiplied together, what is the result?

Guest Jan 21, 2018
 #1
avatar+89715 
+1

18 + 5x^2  =  20x     rewrite as

 

5x^2 -  20x +  18  =  0

 

Complete the square on x

 

5 ( x^2   -  4x  +  18/5)  = 0

 

5 ( x^2  -  4x   +  4   +  18/5  -  4)  = 0

 

5 (  (x - 2)^2   +  18/5  - 20/5 )   =   0

 

5( (x - 2)^2  - 2/5)  = 0

 

(x - 2)^2  -  2/5  =   0

 

(x - 2) ^2   =  2/5           take both roots

 

x -2  = ±√(2/5)

 

x  =    2 ±√(2/5)

 

This evaluates to     x  ≈  1.3675    x  ≈ 2.6325

 

The desired rounding produces     1   and 3     and their product is   3

 

 

cool cool cool

CPhill  Jan 21, 2018

28 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.