若x,y为任意实数,则代数式x²+2x+(y²)²+2y+3的最小值为____?是x²+2x+(y²)²+2y²+3
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/25 19:37:10
![若x,y为任意实数,则代数式x²+2x+(y²)²+2y+3的最小值为____?是x²+2x+(y²)²+2y²+3](/uploads/image/z/5410215-63-5.jpg?t=%E8%8B%A5x%2Cy%E4%B8%BA%E4%BB%BB%E6%84%8F%E5%AE%9E%E6%95%B0%2C%E5%88%99%E4%BB%A3%E6%95%B0%E5%BC%8Fx%26%23178%3B%2B2x%2B%EF%BC%88y%26%23178%3B%EF%BC%89%26%23178%3B%2B2y%2B3%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E4%B8%BA____%3F%E6%98%AFx%26%23178%3B%2B2x%2B%EF%BC%88y%26%23178%3B%EF%BC%89%26%23178%3B%2B2y%26%23178%3B%2B3)
若x,y为任意实数,则代数式x²+2x+(y²)²+2y+3的最小值为____?是x²+2x+(y²)²+2y²+3
若x,y为任意实数,则代数式x²+2x+(y²)²+2y+3的最小值为____?
是x²+2x+(y²)²+2y²+3
若x,y为任意实数,则代数式x²+2x+(y²)²+2y+3的最小值为____?是x²+2x+(y²)²+2y²+3
答:
x²+2x+(y²)²+2y²+3
=(x²+2x+1)+[ (y²)²+2y²+1 ]+ 1
=(x+1)²+(y²+1)²+1
>=0+1+1
=2
当且仅当x=-1,y=0时取得最小值2