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用配方法解几道一元一次方程式,要完整的过程(1) x²+4x=10 (2)x²-6x=11
(3) x²-2x-4=0 ( 4) 6x²-7x+1=0 (5) 5x²-18=9x (6) 4x²-3x=52 (7) 5x²=4-2x
人气:157 ℃ 时间:2019-11-21 03:57:33
解答
(1) x²+4x=10
x²+4x+4=14
(x+2)²=14
x=-2+√14 x=-2-√14
(2)x²-6x=11
x²-6x+9=20
(x-3)²=20
x=3+2√5 x=3-2√5
(3) x²-2x-4=0
x²-2x+1=5
(x-1)²=5
x=1+√5 x=1-√5
( 4) 6x²-7x+1=0
x²-7x/6=-1/6
x²-7x/6+49/144=25/144
(x-7/12)²=(5/12)²
x=7/12+5/12 x=7/12-5/12
x=1 x=1/6
(5) 5x²-18=9x
x²-9x/5=18/5
x²-9x/5+81/100=441/100
(x-9/10)²=(21/10)²
x=9/10+21/10 x=9/10-21/10
x=3 x=-6/5
(6) 4x²-3x=52
x²-3x/4=13
x²-3x/4+9/64=841/64
(x-3/8)²=841/64
∴x=3/8+29/8 x=3/8-29/8
x=4 x=-13/4
(7) 5x²=4-2x
x²+2x/5=4/5
x²+2x/5+1/25=21/25
(x+1/5)²=21/25
∴x=-1/5+√21/5 x=-1/5-√21/5
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