Question

已知 x+y=1,求证：x³+3xy+³=1

Answer 1

题目应是 x+y=1,求证：x³+3xy+y³=1

x+y=1

x^2+2xy+y^2=1

(x+y)(x^2+2xy+y^2)=1*1

x^3+2x^2y+xy^2+x^2y+2xy^2+y^3=1

x^3+3x^2y+3xy^2+y^3=1

x^3+3xy(x+y)+y^3=1

x^3+3xy+y^3=1