如果ax + b = cx + d,x属于R,怎么证明a = c and b = d.

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如果ax + b = cx + d,x属于R,怎么证明a = c and b = d.

如果ax + b = cx + d,x属于R,怎么证明a = c and b = d.
如果ax + b = cx + d,x属于R,怎么证明a = c and b = d.

如果ax + b = cx + d,x属于R,怎么证明a = c and b = d.
证明:
ax+b=cx+d,根据等式性质,可得:
(a-c)x+(b-d)=0,
∵x∈R,即该等式中x不管取何值,等式都成立,那么,
当x=0时,等式也成立,即:
b=d;
此时原式可写成:
(a-c)x=0
因为上式恒成立,因此:
a-c=0,即
a=c
综上:a=c,b=d

ax + b = cx + d

y1 = ax + b
y2 = cx + d

y1 = y2
a = c
b = d

证明:
∵ ax + b = cx + d
∴(a-c)x=(d-b) 1)
要使1)式成立,且x∈R
只有a-c=0,并且d-b=0
所以a=c and b=d