Question

Chứng minh các đẳng thức sau:

a) (a+b+c)^2+(a-b+c)^2+(a+b-c)^2+(b+c-a)^2=4(a^2+b^2+c^2)

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

Answer 1

Bài làm:

a) \(\left(a+b+c\right)^2+\left(a-b+c\right)^2+\left(a+b-c\right)^2+\left(b+c-a\right)^2\)

\(=4\left(a^2+b^2+c^2\right)+2\left(ab+bc+ca+ab-bc-ca+ca-bc-ab+bc-ab-ca\right)\)

\(=4\left(a^2+b^2+c^2\right)+2.0\)

\(=4\left(a^2+b^2+c^2\right)\)

b) \(\left(a+b+c\right)^2+a^2+b^2+c^2\)

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

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

\(=\left(a+b\right)^2+\left(b+c\right)^2+\left(c+a\right)^2\)

Answer 2

vô tkhđ coi hình ảnh nếu k hiện

Answer 3

cam ơn các bạn nhé