巧解方程(1) (x²-1)²-2x²-1=0 (2) (m²+n²)(m²+n²-2)-8=0求m²+n²的值 (3) (x+1分之1)²-2(x+1分之1)-8=0 (4)已知x²+y²+4x-6y+13=0,求x+y的值
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![巧解方程(1) (x²-1)²-2x²-1=0 (2) (m²+n²)(m²+n²-2)-8=0求m²+n²的值 (3) (x+1分之1)²-2(x+1分之1)-8=0 (4)已知x²+y²+4x-6y+13=0,求x+y的值](/uploads/image/z/2769743-47-3.jpg?t=%E5%B7%A7%E8%A7%A3%E6%96%B9%E7%A8%8B%281%29+%28x%26%23178%3B-1%29%26%23178%3B-2x%26%23178%3B-1%3D0+%282%29+%28m%26%23178%3B%2Bn%26%23178%3B%29%28m%26%23178%3B%2Bn%26%23178%3B-2%29-8%3D0%E6%B1%82m%26%23178%3B%2Bn%26%23178%3B%E7%9A%84%E5%80%BC++++%283%29++++++++++%EF%BC%88x%2B1%E5%88%86%E4%B9%8B1%EF%BC%89%26%23178%3B-2%EF%BC%88x%2B1%E5%88%86%E4%B9%8B1%EF%BC%89-8%3D0++++++%EF%BC%884%EF%BC%89%E5%B7%B2%E7%9F%A5x%26%23178%3B%2By%26%23178%3B%2B4x-6y%2B13%3D0%2C%E6%B1%82x%2By%E7%9A%84%E5%80%BC)
巧解方程(1) (x²-1)²-2x²-1=0 (2) (m²+n²)(m²+n²-2)-8=0求m²+n²的值 (3) (x+1分之1)²-2(x+1分之1)-8=0 (4)已知x²+y²+4x-6y+13=0,求x+y的值
巧解方程(1) (x²-1)²-2x²-1=0 (2) (m²+n²)(m²+n²-2)-8=0求
m²+n²的值 (3) (x+1分之1)²-2(x+1分之1)-8=0 (4)已知x²+y²+4x-6y+13=0,求x+y的值
巧解方程(1) (x²-1)²-2x²-1=0 (2) (m²+n²)(m²+n²-2)-8=0求m²+n²的值 (3) (x+1分之1)²-2(x+1分之1)-8=0 (4)已知x²+y²+4x-6y+13=0,求x+y的值
(1) (x²-1)²-2x²-1=0
(x²-1)²-2(x²-1)-3=0
(x²-1-3)(x²+1)=0,
x²-4=0或x²+1=0(无实数根)
X=±2.
(2) (m²+n²)(m²+n²-2)-8=0
(m²+n²)²-2(m²+n²)-8=0,
(m²+n²-4)(m²+n²+2)=0
m²+n²=4.(m²+n²+2≠0).
⑶(x+1分之1)²-2(x+1分之1)-8=0
(X+1/X-4)(X+1/X+2)=0
X+1/X=4或X+1/X+2=0
X²-4x=-1或X²-2X+1=0
(X-2)²=3或(X-1)²=0
X=1或X=2±√3.
(4)已知x²+y²+4x-6y+13=0,
(X+2)²+(Y-3)²=0
X+2=0且Y-3=0,
X=-2,Y=3,
x+y=1.