已知x1+x2=3,x1x2=1,求(1)x1分之1+x2分之1的值.(2)x1分之x2+x2分之x1的值.(3)求(x2+1)/(x1+1)+(x1+1)/(x2+1)的值
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已知x1+x2=3,x1x2=1,求(1)x1分之1+x2分之1的值.(2)x1分之x2+x2分之x1的值.(3)求(x2+1)/(x1+1)+(x1+1)/(x2+1)的值
已知x1+x2=3,x1x2=1,求(1)x1分之1+x2分之1的值.
(2)x1分之x2+x2分之x1的值.
(3)求(x2+1)/(x1+1)+(x1+1)/(x2+1)的值
已知x1+x2=3,x1x2=1,求(1)x1分之1+x2分之1的值.(2)x1分之x2+x2分之x1的值.(3)求(x2+1)/(x1+1)+(x1+1)/(x2+1)的值
(1) 1/x1+1/x2=(x1+x2)/(x1x2)=3/1=3
(2) x2/x1+x1/x2=(x1^2+x2^2)/(x1x2)=x1^2+x2^2+2x1x2-2x1x2=(x1+x2)^2-2=9-2=7
(3) (x2+1)/(x1+1)+(x1+1)/(x2+1)
=[(x2+1)^2+(x1+1)^2]/(x1x2+x1+x2+1)
=[x1^2+x2^2+2(x1+x2)+2]/(1+3+1)
=(x1^2+2x1x2+x2^2-2x1x2+2*3+2)/5
=[(x1+x2)^2-2+8]/5
=15/5
=3
x1+x2=3
两边平方得:
x1²+x2²+2x1x2=9
x1²+x2²=9-2=7
(1)x1分之1+x2分之1
=(x1+x2)/(x1x2)
=3/1
=3
(2)x1分之x2+x2分之x1
=(x1²+x2²)/(x1x2)
=7/1
=7...
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x1+x2=3
两边平方得:
x1²+x2²+2x1x2=9
x1²+x2²=9-2=7
(1)x1分之1+x2分之1
=(x1+x2)/(x1x2)
=3/1
=3
(2)x1分之x2+x2分之x1
=(x1²+x2²)/(x1x2)
=7/1
=7
(3)(x2+1)/(x1+1)+(x1+1)/(x2+1)
=[(x2+1)²+(x1+1)²]/[(x1+1)(x2+1)]
=[(x1²+x2²)+2(x1+x2)+2]/[(x1+x2)+x1x2+1]
=(7+6+2)/(3+1+1)
=15/5
=3
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