已知x,y满足x²+4y²+2x-4y+2=0,求根号5x²+16y²的值
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![已知x,y满足x²+4y²+2x-4y+2=0,求根号5x²+16y²的值](/uploads/image/z/4330860-60-0.jpg?t=%E5%B7%B2%E7%9F%A5x%2Cy%E6%BB%A1%E8%B6%B3x%26%23178%3B%2B4y%26%23178%3B%2B2x-4y%2B2%3D0%2C%E6%B1%82%E6%A0%B9%E5%8F%B75x%26%23178%3B%2B16y%26%23178%3B%E7%9A%84%E5%80%BC)
已知x,y满足x²+4y²+2x-4y+2=0,求根号5x²+16y²的值
已知x,y满足x²+4y²+2x-4y+2=0,求根号5x²+16y²的值
已知x,y满足x²+4y²+2x-4y+2=0,求根号5x²+16y²的值
解
x²+4y²+2x-4y+2=0
(x²+2x+1)+(4y²-4y+1)=0
(x+1)²+(2y-1)²=0
∴x+1=0,2y-1=0
∴x=-1,y=1/2
∴√5x²+16y²
=√5+16×(1/4)
=√5+4
=3
答案是3,x=-1,y=1/2