已知x₁,x₂是方程x²-3x+1=0的两个实数根,则1/x₁+1/x₂的值是A.3 B.-3 C.⅓ D.1请说明为什么
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![已知x₁,x₂是方程x²-3x+1=0的两个实数根,则1/x₁+1/x₂的值是A.3 B.-3 C.⅓ D.1请说明为什么](/uploads/image/z/1592812-28-2.jpg?t=%E5%B7%B2%E7%9F%A5x%26%238321%3B%2Cx%26%238322%3B%E6%98%AF%E6%96%B9%E7%A8%8Bx%26%23178%3B-3x%2B1%3D0%E7%9A%84%E4%B8%A4%E4%B8%AA%E5%AE%9E%E6%95%B0%E6%A0%B9%2C%E5%88%991%2Fx%26%238321%3B%2B1%2Fx%26%238322%3B%E7%9A%84%E5%80%BC%E6%98%AFA.3+B.-3+C.%26%238531%3B+D.1%E8%AF%B7%E8%AF%B4%E6%98%8E%E4%B8%BA%E4%BB%80%E4%B9%88)
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已知x₁,x₂是方程x²-3x+1=0的两个实数根,则1/x₁+1/x₂的值是A.3 B.-3 C.⅓ D.1请说明为什么
已知x₁,x₂是方程x²-3x+1=0的两个实数根,则1/x₁+1/x₂的值是
A.3 B.-3 C.⅓ D.1
请说明为什么
已知x₁,x₂是方程x²-3x+1=0的两个实数根,则1/x₁+1/x₂的值是A.3 B.-3 C.⅓ D.1请说明为什么
由题意知,x1+x2=3 x1x2=1
1/x1+1/x2=x1+x2/x1x2=3/1=3
所以选A
x1+x2=3
x1x2=1
所以原式=(x1+x2)/x1x2=3
1/x₁+1/x₂=(x₁+x₂)/(x₁x₂)=3/1=3
1