当-3≤x≤2时,化简|x-2| + √(x+3)² + √x² - 10x + 25=

问题描述:

当-3≤x≤2时,化简|x-2| + √(x+3)² + √x² - 10x + 25=

x≤2
|x-2|=2-x
√(x+3)² =x+3
√x² - 10x + 25=√(x-5)²=5-x
|x-2| + √(x+3)² + √x² - 10x + 25=
=2-x+x+3+5-x
=10-x

|x-2| + √(x+3)² + √x² - 10x + 25
=|x-2| + √(x+3)² + √(x-5)²
=2-x+x+3+5-x
=10-x

x-2≤0
x+3≥0
x-5所以原式=2-x+|x+3|+√(x-5)²
=2-x+x+3+|x-5|
=5+(5-x)
=10-x