Question

若根号下(x-2)(3-x)=根号下x-2乘根号下3-x化简根号下x²-4x+4+根号下9-6x+x²

Answer 1

算数平方根有意义，x-2≥0 x≥2；3-x≥0 x≤3
2≤x≤3
√(x²-4x+4)+√(9-6x+x²)
=√(x-2)²+√(x-3)²
=x-2+3-x
=1

Answer 2

若根号下(x-2)(3-x)=根号下x-2乘根号下3-x 可知 x-2>=0 3-x >=0 所以 2<= x< =3
根号下x²-4x+4 = 根号下(x-2)^2 = | x - 2| 而2<= x<= 3 所以等于 x-2
根号下9-6x+x² = 根号下(x-3)^2 = | x - 3| 而2<= x<=3 所以等于 3-x
根号下x²-4x+4+根号下9-6x+x² = x-2 + 3-x = 1

Answer 3

若根号下(x-2)(3-x)=根号下x-2乘根号下3-x，说明x-2>=0，3-x>=0，所以 2<=x<=3
所以根号下x²-4x+4=x-2，根号下9-6x+x²=3-x
所以结果为(x-2)(3-x)