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How do you solve this?

 

Find all values of $a$ such that $\frac{a-3}{\sqrt{a}} = -a \sqrt{a}$.

 Aug 25, 2023
 #1
avatar+125628 
+1

(a - 3)  / √a =  -a√a         multiply both sides by √a

 

a - 3  = -a √a * √a       simplify

 

a - 3  =  -a * a

 

a - 3  = -a^2             add a^2 to  both sides

 

a^2 + a  - 3  =  0      complete the square on a ......(you could also use the Q Formula)

 

a^2 + a = 3

 

a^2 + a + 1/4 =  3 + 1/4

 

(a + 1/2)^2   =   13/4         

 (a cannot be negative because we can't have a negative under a radical - take the positive root )

 

a + 1/2  = sqrt (13)  / 2

 

a =  sqrt (13) / 2  - 1/2

 

a = [ sqrt  (13)  - 1 ]   /  2  

 

 

cool cool cool

 Aug 25, 2023

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