Question

若a加b=3,ab=负2,则a的立方加a的平方b加ab的平方加b的立方等于多少

Answer 1

a+b=3,ab=-2

a^3+a^2b+ab^2+b^3

=ab(a+b)+(a+b)(a^2-ab+b^2)

=(a+b)(ab+a^2-ab+b^2)

=(a+b)(a^2+b^2)

=(a+b)[(a+b)^2-2ab]

=3*[3*3-2*(-2)]

=3*13

=39