Question

若x+y+z=5,xy+yz+xz=7,则x^2+y^2+z^2=

Answer 1

若x+y+z=5,xy+yz+xz=7,则
x^2+y^2+z^2
=(x+y+z)²-2(xy+yz+xz)
=25-14
=11

Answer 2

5^2-7×2=11
x^2+y^2+z^2=（x+y+z）^2-2（xy+yz+xz）

Answer 3

9 (x+y+z)^2=x^2+y^2+z^2+2(xy+yz+xz) 带入求得

Answer 4

这个题目这样想:
若x+y+z=5,xy+yz+xz=7,则
x^2+y^2+z^2
=(x+y+z)²-2(xy+yz+xz)
=25-14
=11

Answer 5

(x+y+z)^2
=x^2 +y^2 +z^2 +2xy+2xz+2yz
=x^2 +y^2 +z^2 +2(xy+yz+xz)

已知x+y+z=5，xy+yz+xz=7，代入就行了

5^2=x^2 + y^2 + z^2 + 2*7
25=x^2 + y^2 + z^2 +14
x^2 + y^2 + z^2 = 25-14
x^2 + y^2 + z^2 = 11

Answer 6

因为（x+y+z)²=x²+y²+z²+2(xy+yz+xz）
所以则x^2+y^2+z^2=(x+y+z)²-2(xy+yz+xz)=25-14=11