Question 644483
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a³ + b³ = 72
 
a³ + [(a²-12)<sup>1/2</sup>]³ = 72
 
a³ + (a²-12)<sup>3/2</sup> = 72
        (a²-12)<sup>3/2</sup> = 72 - a³
 
Square both sides
 
[(a²-12)<sup>3/2</sup>]² = (72-a³)²
 
             (a²-12)³ =  5184-144a³+a<sup>6</sup>
 
(a²)³-3(a²)²(12) + 3(a²)(12) ² -(12)³ = 5184 - 144a³ + a<sup>6</sup> 
 
a<sup>6</sup>-36a<sup>4</sup> + 3(a²)(144) - 1728 = 5184-144a³+a<sup>6</sup>
 
a<sup>6</sup>-36<sup>4</sup> + 432a² - 1728 = 5184-144a³+a<sup>6</sup>
 
-36a<sup>4</sup> + 144a³ + 432a² - 6912 = 0
 
Divide through by -36
 
a<sup>4</sup> - 4a³ - 12a² + 192 = 0
 
Edwin
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