若x²+4y²+2x-4y+2=0,则5x²+16y²的值是多少?
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![若x²+4y²+2x-4y+2=0,则5x²+16y²的值是多少?](/uploads/image/z/5255136-0-6.jpg?t=%E8%8B%A5x%26%23178%3B%2B4y%26%23178%3B%2B2x-4y%2B2%3D0%2C%E5%88%995x%26%23178%3B%2B16y%26%23178%3B%E7%9A%84%E5%80%BC%E6%98%AF%E5%A4%9A%E5%B0%91%3F)
若x²+4y²+2x-4y+2=0,则5x²+16y²的值是多少?
若x²+4y²+2x-4y+2=0,则5x²+16y²的值是多少?
若x²+4y²+2x-4y+2=0,则5x²+16y²的值是多少?
解
x²+4y²+2x-4y+2=0
(x²+2x+1)+(4y²-4y+1)=0
(x+1)²+(2y-1)²=0
∵(x+1)²≥0
(2y-1)²≥0
∴x+1=0
2y-1=0
∴x=-1,y=1/2
∴5x²+16y²
=5+4
=9
转换为(x+1)²+(2y-1)²=0
x=-1;y=1/2;
5x²+16y²=9;