已知实数x,y满足:1+|x-1|=√[1-(y+1)^2],则x^2+y^2等于多少?
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![已知实数x,y满足:1+|x-1|=√[1-(y+1)^2],则x^2+y^2等于多少?](/uploads/image/z/5529904-16-4.jpg?t=%E5%B7%B2%E7%9F%A5%E5%AE%9E%E6%95%B0x%2Cy%E6%BB%A1%E8%B6%B3%3A1%2B%7Cx-1%7C%3D%E2%88%9A%5B1-%EF%BC%88y%2B1%29%5E2%5D%2C%E5%88%99x%5E2%2By%5E2%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F)
已知实数x,y满足:1+|x-1|=√[1-(y+1)^2],则x^2+y^2等于多少?
已知实数x,y满足:1+|x-1|=√[1-(y+1)^2],则x^2+y^2等于多少?
已知实数x,y满足:1+|x-1|=√[1-(y+1)^2],则x^2+y^2等于多少?
答:
1+|x-1|=√[1-(y+1)^2]>=1
后面一个不等式两边平方得:1-(y+1)^2>=1
(y+1)^2<=0
所以:
y+1=0
解得:y=-1
代入原式得:1+|x-1|=1
解得:x=1
所以:x^2+y^2=2
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