已知一元二次方程x^2+3x-1=0的两个根是x1,x2,不解方程,求下列代数式的值1/x1^2+1/x2^2 和|x1-x2|
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![已知一元二次方程x^2+3x-1=0的两个根是x1,x2,不解方程,求下列代数式的值1/x1^2+1/x2^2 和|x1-x2|](/uploads/image/z/3713550-6-0.jpg?t=%E5%B7%B2%E7%9F%A5%E4%B8%80%E5%85%83%E4%BA%8C%E6%AC%A1%E6%96%B9%E7%A8%8Bx%5E2%2B3x-1%3D0%E7%9A%84%E4%B8%A4%E4%B8%AA%E6%A0%B9%E6%98%AFx1%2Cx2%2C%E4%B8%8D%E8%A7%A3%E6%96%B9%E7%A8%8B%2C%E6%B1%82%E4%B8%8B%E5%88%97%E4%BB%A3%E6%95%B0%E5%BC%8F%E7%9A%84%E5%80%BC1%2Fx1%5E2%2B1%2Fx2%5E2+++%E5%92%8C%7Cx1-x2%7C)
已知一元二次方程x^2+3x-1=0的两个根是x1,x2,不解方程,求下列代数式的值1/x1^2+1/x2^2 和|x1-x2|
已知一元二次方程x^2+3x-1=0的两个根是x1,x2,不解方程,求下列代数式的值
1/x1^2+1/x2^2 和|x1-x2|
已知一元二次方程x^2+3x-1=0的两个根是x1,x2,不解方程,求下列代数式的值1/x1^2+1/x2^2 和|x1-x2|
已知一元二次方程x^2+3x-1=0的两个根是x1,x2
∴x1+x2=-3,x1·x2=-1
1/x1^2+1/x2^2
=(x2²+x1²)/(x1·x2)²
=[(x1+x2)²-2x1·x2]/(x1·x2)²
=[(-3)²-2×(-1)]÷(-1)²
=11
(x1-x2)²=(x1+x2)²-4x1·x2
=(-3)²-4×(-1)
=13
|x1-x2|=√13
x1*x2=-1/2,x1+x2=-3/2;
(1)=x1*x2-(x1+x2)+1=2;
(2)=x1*x2(x1^2+x2^2)=x1*x2[(x1^2+x2^2+2x1*x2)-2x1*x2]=x1*x2[(x1+x2)^2-2x1*x2]=-13/8
x1+x2=-3,
x1x2=-1
1/x1^2+1/x2^2=(x1^2+x2^2)/(x1x2)^2=[(x1+x2)^2-2x1x2]/(x1x2)^2=[9+2]/1^2=11
|x1-x2|^2=(x1+x2)^2-4x1x2=9+4=13
因此|x1-x2|=√13
x1+x2=-3
x1x2=-1
1/x1^2+1/x2^2
=(x1^2+x2^2)/(x1x2)^2
= [(x1+x2)^2-2x1x2]
=·[9+2]
=11
|x1-x2|=√(x1-x2)^2
=√[(x1+x2)^2-4x1x2]
=√(9+4)
=√13