已知a是4倍根号3的小数部分，求（a-1分之1-2a+a²）+a²+a分之根号a平方-2a+1
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解决时间 2021-04-04 12:23
- 提问者网友：箛茗
- 2021-04-04 01:31
已知a是4倍根号3的小数部分，求（a-1分之1-2a+a²）+a²+a分之根号a平方-2a+1
最佳答案
- 五星知识达人网友：傲气稳了全场
- 2021-04-04 02:48
(1-2a+a^2)/(a-1)+(a^2-2a+1)/(a^2+a)
=(a-1)^2/(a-1)+(a-1)^2/a(a+1)
=(a-1)+(a-1)^2/a(a+1)
=(a-1)+[(a+1)^2-4a]/a(a+1)
=(a-1)+(a+1)/a-4/(a+1)
=(a-1)+1+1/a-4/(a+1)
=a+1/a-4/(a+1)
a=4V3-6
原式=(4V3-6)+1+1/(4V3-6)-4/(4V3-5)
=4V3-6+1+(4V3+6)/(48-36)-4/(4V3-5)
=4V3-5+(4V3+6)/12-4(4V3+5)/(48-25)
=4V3-5+1/3V3+1/2-(16V3+20)/23
=(4+1/3-16/23)V3+(1/2-5-20/23)
=(a-1)^2/(a-1)+(a-1)^2/a(a+1)
=(a-1)+(a-1)^2/a(a+1)
=(a-1)+[(a+1)^2-4a]/a(a+1)
=(a-1)+(a+1)/a-4/(a+1)
=(a-1)+1+1/a-4/(a+1)
=a+1/a-4/(a+1)
a=4V3-6
原式=(4V3-6)+1+1/(4V3-6)-4/(4V3-5)
=4V3-6+1+(4V3+6)/(48-36)-4/(4V3-5)
=4V3-5+(4V3+6)/12-4(4V3+5)/(48-25)
=4V3-5+1/3V3+1/2-(16V3+20)/23
=(4+1/3-16/23)V3+(1/2-5-20/23)
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