![27x^3+8y^3=(3x)^3+(2y)^3=(3x+2y)[(3x)^2-3x\cdot2y+(2y)^2]\\\\=(3x+2y)[(3x)^2+2\cdot3x\cdot2y+(2y)^2-3\cdot3x\cdot2y]\\\\=(3x+2y)[(3x+2y)^2-18xy]=(*)\\---------------------------\\3x+2y=20\\\\xy=\frac{14}{9}\\------------------------------\\(*)=20\cdot(20^2-19\cdot\frac{14}{9})=20\cdot(400-18\cdot\frac{14}{9})=20\cdot(400-2\cdot14)\\\\=20\cdot(400-28)=20\cdot372=7440](/tpl/images/0213/6463/c20ce.png)
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if 3x+2y = 20 and xy =...
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