Question

用配方法解下列方程

①2X²+6=7X
②3X²-9X+2=0
③6X²-7X+1=0
④5X²-18=9X
⑤4X²-3X=52
⑥5X²=4-2x
⑦X²-3X+1=0

Answer 1

①2X²+6=7X
2X²-7X+6=0
2(X²-7/2X)+6=0
2(X²-7/2X+49/16)-2×49/16+6=0
2(X-7/4)²-1/8=0
(X-7/4)²=1/16
X-7/4=±1/4
X=1/4+7/4=2
X=-1/4+7/4=6/4=3/2
②3X²-9X+2=0
3(X²-3X+9/4)-3×9/4+2
3(X-3/2)²=19/4
(X-3/2)²=19/12
X-3/2=±√57/6
X=(9+√57)/6
X=(9-√57)/6
③6X²-7X+1=0
6(X²-7/6)+1=0
6(X-7/12)²-49/24+1=0
(X-7/12)²=25/144
X-7/12=±5/12
X=1
X=1/6
④5X²-18=9X
5(X²-9/5X)-18=0
5(X-9/10)²-5×81/100-18=0
5(X-9/10)²=2205/100
(X-9/10)²=441/100
X-9/10=±21/10
X=3
X=-12/10=-6/5
⑤4X²-3X=52
4(X²-3/4X)=52
4(X-3/8)²=52+4×9/64
(X-3/8)²=841/64
X-3/8=8√841/8
X=(3+√841)/8
X=(3-√841)/8

⑥5X²=4-2x
5(X+1/5)²=4+1/5
5(X+1/5)²=21/5
X+1/5=±√21/5
X=(-1+√21)/5
X=(-1-√21)/5

⑦X²-3X+1=0
(X-3/2)²=5/4
X-3/2=±√5/2
X=(3+√5)/2
X=(3-√5)/2