Question

[Phan Hà Thanh]

Chứng minh rằng:

a) \(\left(x+y\right)^5-x^5-y^5=5xy\left(x+y\right)\left(x^2+xy+y^2\right)\)

b) Cho a + b + c = 0. CMR: \(\left(ab+bc+ca\right)^2=a^2b^2+b^2c^2+c^2a^2\)

Answer 1

[svtkvtm]

\(\left(ab+bc+ca\right)^2=a^2b^2+2ab^2c+2a^2bc+b^2c^2+2c^2ba+c^2a^2=\left(a^2b^2+b^2c^2+c^2a^2\right)+2abc\left(a+b+c\right)=a^2b^2+b^2c^2+c^2a^2\)