(1)x²+10x+ 16=0 (2)x²-x-3/4=0 (3)3x²+6x-5=0 (
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(1)x²+10x+ 16=0 (2)x²-x-3/4=0 (3)3x²+6x-5=0 (4)3x²-x-9=0
配方法解方程:
(1)
x²+10x+16 = 0 ,
(x+5)² = x²+10x+25 = x²+10x+16+9 = 9 ,
x+5 = 3 或 x+5 = -3 ,
解得:x = -2 或 x = -8 ;
(2)
x²-x-3/4 = 0 ,
(x-1/2)² = x²-x+1/4 = x²-x-3/4+1 = 1 ,
x-1/2 = 1 或 x-1/2 = -1 ,
解得:x = 3/2 或 x = -1/2 ;
(3)
3x²+6x-5 = 0 ,
3(x²+2x)-5 = 0 ,
3(x+1)² = 3x²+6x+3 = 3x²+6x-5+8 = 8 ,
(x+1)² = 8/3 ,
x+1 = (2/3)√6 或 x+1 = -(2/3)√6 ,
解得:x = -1+(2/3)√6 或 x = -1-(2/3)√6 ;
(4)
3x²-x-9 = 0 ,
3(x²-x/3)-9 = 0 ,
3(x-1/6)² = 3x²-x+1/12 = 3x²-x-9+109/12 = 109/12 ,
(x-1/6)² = 109/36 ,
x-1/6 = (1/6)√109 或 x-1/6 = -(1/6)√109 ,
解得:x = (1+√109)/6 或 x = (1-√109)/6 .
(1)
x²+10x+16 = 0 ,
(x+5)² = x²+10x+25 = x²+10x+16+9 = 9 ,
x+5 = 3 或 x+5 = -3 ,
解得:x = -2 或 x = -8 ;
(2)
x²-x-3/4 = 0 ,
(x-1/2)² = x²-x+1/4 = x²-x-3/4+1 = 1 ,
x-1/2 = 1 或 x-1/2 = -1 ,
解得:x = 3/2 或 x = -1/2 ;
(3)
3x²+6x-5 = 0 ,
3(x²+2x)-5 = 0 ,
3(x+1)² = 3x²+6x+3 = 3x²+6x-5+8 = 8 ,
(x+1)² = 8/3 ,
x+1 = (2/3)√6 或 x+1 = -(2/3)√6 ,
解得:x = -1+(2/3)√6 或 x = -1-(2/3)√6 ;
(4)
3x²-x-9 = 0 ,
3(x²-x/3)-9 = 0 ,
3(x-1/6)² = 3x²-x+1/12 = 3x²-x-9+109/12 = 109/12 ,
(x-1/6)² = 109/36 ,
x-1/6 = (1/6)√109 或 x-1/6 = -(1/6)√109 ,
解得:x = (1+√109)/6 或 x = (1-√109)/6 .
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