作业帮如何做这两道题
来源：学生作业帮 编辑：作业帮 分类：数学作业 时间：2024/04/29 16:05:21
如何做这两道题
1.x^2 + y^2 + z^2 - 2x + 4y - 6z + 14
=(x^2 - 2x + 1) + (y^2 + 4y + 4) + (z^2 - 6z + 9)
=(x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 0
所以,x = 1,y = -2,z = 3.则 x + y + z = 2
2.ab(c^2 + d^2) + cd(a^2 + b^2)
=abc^2 + abd^2 + cda^2 + cdb^2
=ac*bc + ad * bd + ac * ad + bc * bd
=ac * (bc + ad) + bd * (ad + bc)
=(ac + bd) * (bc + ad)
= 0 * (bc + ad)
= 0
=(x^2 - 2x + 1) + (y^2 + 4y + 4) + (z^2 - 6z + 9)
=(x - 1)^2 + (y + 2)^2 + (z - 3)^2 = 0
所以,x = 1,y = -2,z = 3.则 x + y + z = 2
2.ab(c^2 + d^2) + cd(a^2 + b^2)
=abc^2 + abd^2 + cda^2 + cdb^2
=ac*bc + ad * bd + ac * ad + bc * bd
=ac * (bc + ad) + bd * (ad + bc)
=(ac + bd) * (bc + ad)
= 0 * (bc + ad)
= 0