x-y=5,y-z=3,x+z=4,求x^2-z^2

x-y=5,y-z=3
=>x-y+(y-z)=x-z=5+3=8.
x^2-z^2=(x-z)(x+z)
=>x^2-z^2=8*4=32.

第一式和第二式相加，得x-z=8
再与第三式相乘，得x^2-z^2=32

x-y=5,y-z=3,y=z+3,x-(z+3)=5,x-z=8,x+z=4,2x=12,x=6,z=4-6=-2,x^2-z^2=36-4=32

解：
x-y=5,（1)

y-z=3,y=z+3``(2）

(2)带入(1)x-z=8(3)

又因为x+z=4

所以x=6,z=-2

x^2-z^2=36-4=32

x^2-z^2=(x+z)(x-z)

又因x-y=5,y-z=3,x+z=4，故，x-z=8,x+z=4,所以答案为8×4＝32

x^2-z^2=(x+z)(x-z)
=(x+z)[(x-y)+(y-z)]
=4*(5+3)
=32