SOLUTION: please explain b = (a^²-12)^1/2 Substituting this positive square root and simplifying gives this: a^4 - 4a^3 - 12a^2 + 192 = 0 how this happened?

Algebra ->  Square-cubic-other-roots -> SOLUTION: please explain b = (a^²-12)^1/2 Substituting this positive square root and simplifying gives this: a^4 - 4a^3 - 12a^2 + 192 = 0 how this happened?       Log On


   

Question 644483: please explain
b = (a^²-12)^1/2
Substituting this positive square root and simplifying gives
this:
a^4 - 4a^3 - 12a^2 + 192 = 0 how this happened?
Answer by Edwin McCravy(20081) About Me  (Show Source):
You can put this solution on YOUR website!
a³ + b³ = 72
 
a³ + [(a²-12)1/2]³ = 72
 
a³ + (a²-12)3/2 = 72
        (a²-12)3/2 = 72 - a³
 
Square both sides
 
[(a²-12)3/2]² = (72-a³)²
 
             (a²-12)³ =  5184-144a³+a6
 
(a²)³-3(a²)²(12) + 3(a²)(12) ² -(12)³ = 5184 - 144a³ + a6 
 
a6-36a4 + 3(a²)(144) - 1728 = 5184-144a³+a6
 
a6-364 + 432a² - 1728 = 5184-144a³+a6
 
-36a4 + 144a³ + 432a² - 6912 = 0
 
Divide through by -36
 
a4 - 4a³ - 12a² + 192 = 0
 
Edwin