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Find all values of a that satsify the equation \frac{a}{3} + 1 = \frac{a + 3}{a} + 1.

 Jun 5, 2024
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\( \frac{a}{3} + 1 = \frac{a + 3}{a} + 1 \)

 

a/3 = (a + 3) / a       cross-multiply

 

a^2  = 3(a + 3)

 

a^2  = 3a + 9

 

a^2 - 3a  = 9

 

a^2 -3a + 9/4 = 9 + 9/4

 

(a - 3/2)^2  = 45 / 4      take both roots

 

a - 3/2  =  + / -  3sqrt 5 / 2

 

a = [ 3 +/- 3sqrt 5 ] / 2

 

cool cool cool

 Jun 6, 2024

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