解下列方程:
(1)x2-4x-45=0;
(2)8y2-2=4y(配方法);
(3)2(x2-1)=3(x-1);
(4)2x2-4x-5=0(公式法).
解:(1)(x-9)(x+5)=0,
∴x-9=0或x+5=0,
解得x
1=9,x
2=-5;
(2)8y
2-4y-2=0,
y
2-
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y=
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,
y
2-
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y+
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=
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,
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=
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,
y-
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=±
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,
y=
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±
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,
∴y
1=
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,y
2=
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;
(3)2(x+1)(x-1)-3(x-1)=0,
(x-1)(2x+2-3)=0,
∴x-1=0或2x-1=0,
解得x
1=1,x
2=
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;
(4)2x
2-4x-5=0,
a=2,b=-4,c=-5,
△=16+40=56,
x=
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,
∴x
1=1+
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,x
2=1-
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.
分析:(1)用十字相乘法因式分解求出方程的根.
(2)按照題目的要求,化二次項的系數為1,把常數項移到右邊,用配方法解方程.
(3)把右邊的項移到左邊,整理方程后,用提公因式法因式分解求出方程的根.
(4)用一元二次方程的求根公式求出方程的根.
點評:本題考查的是解一元二次方程,根據題目的結構特點和要求,選擇適當的方法解方程,(1)題用十字相乘法因式分解求出方程的根.(2)按照題目的要求用配方法求出方程的根.(3)把右邊的項移到左邊用提公因式法因式分解求出方程的根.(4)用一元二次方程的求根公式求出方程的根.