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求实数xyz使它们同时满足2x+3y+z=13…(1)4x2+9y2+z2-2x+15y+3z=82…(2).

题目详情
求实数x y z 使它们同时满足2x+3y+z=13…(1) 4x 2 +9y 2 +z 2 -2x+15y+3z=82…(2).
▼优质解答
答案和解析
解析:可令x 1 =2x x 2 =3y+3 x 3 =z+2 则x 1 +x 2 +x 3 =18且x 1 2 +x 2 2 +x 3 2 =108,由此及柯西不等式得18 2 =(x 1 +x 2 +x 3 ) 2 ≤(x 1 2 +x 2 2 +x 3 2 ) 2 (1 2 +1 2 +1 2 )=108×3 上式等...