4道题怎么做? 15
要在24小时内回答,4道题区分开来一起回答,回答需完整、正确,急!!!高悬赏,只要是满足以上3个条件的第一个回答者就会采纳...
要在24小时内回答,4道题区分开来一起回答,回答需完整、正确,急!!!高悬赏,只要是满足以上3个条件的第一个回答者就会采纳
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1. x+1/x = 3,
(1) x^2 + 1/x^2 = (x+1/x)^2 - 2 = 9-2 = 7
(2) x^3 + 1/x^3 = (x+1/x)^3 - 3x - 3/x = (x+1/x)^3 - 3(x +1/x) = 3^3 - 3·3 = 18
2. m^2-5m-1 = 0, m^2 = 5m+1
(m^4+1)/m^2 = [(5m+1)^2+1]/(5m+1) = (25m^2+10m+2)/(5m+1)
=[25(5m+1)+2(5m+1)]/(5m+1) = 25+2 = 27
3. x/(x^2+x+1) = 1/4, x^2+x+1 = 4x, x^2 = 3x-1,
x^2/(x^4+x^2+1) = (3x-1)/[(3x-1)^2+(3x-1)+1] = (3x-1)/(9x^2-6x+1+3x)
= (3x-1)/[9(3x-1)-(3x-1)] = 1/(9-1) = 1/8
(1) x^2 + 1/x^2 = (x+1/x)^2 - 2 = 9-2 = 7
(2) x^3 + 1/x^3 = (x+1/x)^3 - 3x - 3/x = (x+1/x)^3 - 3(x +1/x) = 3^3 - 3·3 = 18
2. m^2-5m-1 = 0, m^2 = 5m+1
(m^4+1)/m^2 = [(5m+1)^2+1]/(5m+1) = (25m^2+10m+2)/(5m+1)
=[25(5m+1)+2(5m+1)]/(5m+1) = 25+2 = 27
3. x/(x^2+x+1) = 1/4, x^2+x+1 = 4x, x^2 = 3x-1,
x^2/(x^4+x^2+1) = (3x-1)/[(3x-1)^2+(3x-1)+1] = (3x-1)/(9x^2-6x+1+3x)
= (3x-1)/[9(3x-1)-(3x-1)] = 1/(9-1) = 1/8
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4)、a+b+c=0
a平方+b平方+c平方=1
(a+b+c)平方
=a平+b平方+c平方
+2ab+2bc+2ca
=1+2(ab+bc+ca)
=0平方=0
所以1+2(ab+bc+ca)=0
ab+bc+ca=-1/2
a平方+b平方+c平方=1
(a+b+c)平方
=a平+b平方+c平方
+2ab+2bc+2ca
=1+2(ab+bc+ca)
=0平方=0
所以1+2(ab+bc+ca)=0
ab+bc+ca=-1/2
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