Câu hỏi của Cường Hoàng

Question

Cho a + b + c + d = 0. Hãy viết $a^2+b^2+c^2+d^2$ dưới dạng tổng 3 bình phương.

Hung nguyen · Accepted Answer

Ta có:

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

$=2\left(b^2+c^2+d^2\right)+2\left(bd+cd+bc\right)$

$=\left(b^2+2bc+c^2\right)+\left(c^2+2cd+d^2\right)+\left(d^2+2db+b^2\right)$

$=\left(b+c\right)^2+\left(c+d\right)^2+\left(d+b\right)^2$Câu trả lời: Ta có:

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

$=2\left(b^2+c^2+d^2\right)+2\left(bd+cd+bc\right)$

$=\left(b^2+2bc+c^2\right)+\left(c^2+2cd+d^2\right)+\left(d^2+2db+b^2\right)$

$=\left(b+c\right)^2+\left(c+d\right)^2+\left(d+b\right)^2$

Bài 1: Căn bậc hai