(40-x)^2+(50-x)^2=(40+x)^2怎么解

问题描述:

(40-x)^2+(50-x)^2=(40+x)^2怎么解

(40-x)^2+(50-x)^2=(40+x)^2
(40-x)²-(40+x)²+(50-x)²=0
(40-x+40+x)(40-x-40-x)+(50-x)²=0
80(-2x)+(x-50)²=0
x²-100x+2500-160x=0
x²-260x+2500=0
(x-10)(x-250)=0
x=10 or x=250

(40-x)^2+(50-x)^2=(40+x)^2
(40-x)^2-(40+x)^2+(50-x)^2=0
[(40-x)-(40+x)][(40-x)+(40+x)]+(50-x)^2=0
(40-x-40-x)(40-x+40+x)+(50-x)^2=0
-2x*80+x^2-100x+2500=0
x^2-260x+2500=0
(x-250)(x-10)=0
x=250或x=10