Question

已知x,y为实数,且实数m满足关系式根号3x+5y-2-m加根号2x+3y-m=根号x-196+y乘根号196-x-y,

Answer 1

已知,√(3x+5y-2-m)+√(2x+3y-m) = √(x-196+y)*√(196-x-y) ,

考察等式右边的定义域：x-196+y ≥ 0 ,196-x-y ≥ 0 ,

因为,x-196+y 和 196-x-y 互为相反数,

所以,x-196+y = 196-x-y = 0 ,

则有：x+y = 196 ,

可得：√(3x+5y-2-m)+√(2x+3y-m) = 0 ；

即有：3x+5y-2-m = 0 ,2x+3y-m = 0 ,

可得：3x+5y-2 = m = 2x+3y ,

整理得：x+2y = 2 ,

而且,x+y = 196 ,

可得：m = 2x+3y = (x+2y)+(x+y) = 198 .