若x1和x2是方程x^2+5x-3=0的两根,求值:(1) |x1-x2| (2)1\x1^2+1\x2^2
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![若x1和x2是方程x^2+5x-3=0的两根,求值:(1) |x1-x2| (2)1\x1^2+1\x2^2](/uploads/image/z/4350017-65-7.jpg?t=%E8%8B%A5x1%E5%92%8Cx2%E6%98%AF%E6%96%B9%E7%A8%8Bx%5E2%2B5x-3%3D0%E7%9A%84%E4%B8%A4%E6%A0%B9%2C%E6%B1%82%E5%80%BC%EF%BC%9A%EF%BC%881%29+%7Cx1-x2%7C+%282%291%5Cx1%5E2%2B1%5Cx2%5E2)
若x1和x2是方程x^2+5x-3=0的两根,求值:(1) |x1-x2| (2)1\x1^2+1\x2^2
若x1和x2是方程x^2+5x-3=0的两根,求值:(1) |x1-x2| (2)1\x1^2+1\x2^2
若x1和x2是方程x^2+5x-3=0的两根,求值:(1) |x1-x2| (2)1\x1^2+1\x2^2
x1+x2=-5,x1x2=-3
1)|x1-x2|^2=(x1+x2)^2-4x1x2=25+12=37
|x1-x2|=√37
2)1/x1^2+1/x2^2=(x1^2+x2^2)/(x1x2)^2=[(x1+x2)^2-2x1x2]/(x1x2)^2=[25+6]/9=31/9