①若x²+2x²+y²-8y+17=0,求2x-y的值
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①若x²+2x²+y²-8y+17=0,求2x-y的值
②已知(x²+y²)×(x²+y²-6)+9=0,求x²+y²的值.
用完全平方公式分解因式.
②已知(x²+y²)×(x²+y²-6)+9=0,求x²+y²的值.
用完全平方公式分解因式.
![①若x²+2x²+y²-8y+17=0,求2x-y的值](/uploads/image/z/19315266-42-6.jpg?t=%E2%91%A0%E8%8B%A5x%26sup2%3B%2B2x%26sup2%3B%2By%26sup2%3B-8y%2B17%3D0%2C%E6%B1%822x-y%E7%9A%84%E5%80%BC)
1
x^2+2x+y^2-8y+17=0
x^2+2x+1+y^2-8y+16=0
(x+1)^2+(y-4)^2=0
(x+1)^2≥0,(y-4)^2≥0,(x+1)^2+(y-4)^2≥0
当且仅当(x+1)^2=0,(y-4)^2=0
(x+1)^2+(y-4)^2=0
x=-1,y-4
2x-y=-6
2
(x²+y²)(x²+y²-6)+9=0
(x²+y²)²-6(x²+y²)+9=0
(x²+y²-3)²=0
x²+y²=3
x^2+2x+y^2-8y+17=0
x^2+2x+1+y^2-8y+16=0
(x+1)^2+(y-4)^2=0
(x+1)^2≥0,(y-4)^2≥0,(x+1)^2+(y-4)^2≥0
当且仅当(x+1)^2=0,(y-4)^2=0
(x+1)^2+(y-4)^2=0
x=-1,y-4
2x-y=-6
2
(x²+y²)(x²+y²-6)+9=0
(x²+y²)²-6(x²+y²)+9=0
(x²+y²-3)²=0
x²+y²=3
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