Question

Find the value of:


`27x^(3)+8 y^(3)` if 3x+2y = 20 and xy = 
`(14)/(9)`

Answer 1

`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=(14)/(9)\\------------------------------\\(*)=20\cdot(20^2-19\cdot(14)/(9))=20\cdot(400-18\cdot(14)/(9))=20\cdot(400-2\cdot14)\\\\=20\cdot(400-28)=20\cdot372=7440`




`a^3+b^3=(a+b)(a^2-ab+b^2)\\\\(a+b)^2=a^2+2ab+b^2`