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For which positive integer values of \(k\) does \(kx^2+20x+k\) have rational solutions? Express your answers separated by commas and in increasing order.

off-topic
 Jul 21, 2019
edited by EvanWei123  Jul 21, 2019
edited by EvanWei123  Jul 21, 2019
 #1
avatar+143 
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This is not a off topic post, i just accidently clicked it.

 Jul 21, 2019
 #2
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It's fine.

tommarvoloriddle  Jul 22, 2019
 #3
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For rational solutions b^2-4ac must be a perfect square

 

\(b^2-4ac=20^2-4k^2\\ b^2-4ac=400-4k^2\\ b^2-4ac=4(100-k^2)\\ \)

 

so 100 - k^2 must be a perfect square

 

k=6, 8  are the only 2 that work.

 

100-36=64

100-64=36

 Jul 24, 2019
 #4
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Thank you melody :D

 Jul 26, 2019

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