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设方程x²+x-1=0的两个根是x1,x2,求4x1^5+10x2^3的值
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设方程x²+x-1=0的两个根是x1,x2,求4x1^5+10x2^3的值
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答案和解析
x1+x2=-1, x1x2=-1
4x1^5+10x2^3
=4*(x1^2*x1^2*x1)+10*(x2^2*x2)
=4*(1-x1)^2*x1+10*(1-x2)*x2
=4(x1^2-2x1+1)*x1+10(x2+x2-1)
=4(1-x1-2x1+1)*x1+10(2x2-1)
=4(2-3x1)*x1+10(2x2-1)
=4(2x1+3x1-3)+10(2x2-1)
=20x1-12+20x2-10
=20(x1+x2)-22
=-20-22=-42
4x1^5+10x2^3
=4*(x1^2*x1^2*x1)+10*(x2^2*x2)
=4*(1-x1)^2*x1+10*(1-x2)*x2
=4(x1^2-2x1+1)*x1+10(x2+x2-1)
=4(1-x1-2x1+1)*x1+10(2x2-1)
=4(2-3x1)*x1+10(2x2-1)
=4(2x1+3x1-3)+10(2x2-1)
=20x1-12+20x2-10
=20(x1+x2)-22
=-20-22=-42
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