设方程x^2-7x+8=0的两根为x1,x2,不解方程求下列代数式的值
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x1+x2=7 x1x2=8
(1)
x1^3-8x1^2+15x1-8
=x1^3-x1^3x2+(x1+x2+x1x2)x1-x1x2
=x1^3-x1^3x2+x1^2+x1^2x2
=x1^3(1-x2)+x1^2(1+x2)
=x1^2(x1-x1x2+1+x2)
=x1^2(x1+x2-x1x2+1)
=x1^2(7-8+1)
=0
(2)
[1/(x1-6)]-x2/2
=[2-x2(x1-6)]/[2(x1-6)]
=[2-x1x2+6x2]/[2(x1-7+1)]
=[2-8+6x2]/[2(x1-x1-x2+1)]
=6(x2-1)/[2(1-x2)]
=-3
(1)
x1^3-8x1^2+15x1-8
=x1^3-x1^3x2+(x1+x2+x1x2)x1-x1x2
=x1^3-x1^3x2+x1^2+x1^2x2
=x1^3(1-x2)+x1^2(1+x2)
=x1^2(x1-x1x2+1+x2)
=x1^2(x1+x2-x1x2+1)
=x1^2(7-8+1)
=0
(2)
[1/(x1-6)]-x2/2
=[2-x2(x1-6)]/[2(x1-6)]
=[2-x1x2+6x2]/[2(x1-7+1)]
=[2-8+6x2]/[2(x1-x1-x2+1)]
=6(x2-1)/[2(1-x2)]
=-3
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