问题
填空题
若(x2+y2)4-8(x2+y2)2+16=0,则x2+y2=______.
答案
∵(x2+y2)4-2×(x2+y2)2×4+42=0,
∴[(x2+y2)2-4]2=0,
∴x2+y2-4=0,
∴x2+y2=4.
若(x2+y2)4-8(x2+y2)2+16=0,则x2+y2=______.
∵(x2+y2)4-2×(x2+y2)2×4+42=0,
∴[(x2+y2)2-4]2=0,
∴x2+y2-4=0,
∴x2+y2=4.