2*sqrt(3-2*sqrt(2))+sqrt(17-12*sqrt(2))等于多少上面的sqrt是根号的意思,求这道题怎么解,最后得数是1,
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![2*sqrt(3-2*sqrt(2))+sqrt(17-12*sqrt(2))等于多少上面的sqrt是根号的意思,求这道题怎么解,最后得数是1,](/uploads/image/z/1667058-42-8.jpg?t=2%2Asqrt%283-2%2Asqrt%282%29%29%2Bsqrt%2817-12%2Asqrt%282%29%29%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%E4%B8%8A%E9%9D%A2%E7%9A%84sqrt%E6%98%AF%E6%A0%B9%E5%8F%B7%E7%9A%84%E6%84%8F%E6%80%9D%2C%E6%B1%82%E8%BF%99%E9%81%93%E9%A2%98%E6%80%8E%E4%B9%88%E8%A7%A3%2C%E6%9C%80%E5%90%8E%E5%BE%97%E6%95%B0%E6%98%AF1%2C)
2*sqrt(3-2*sqrt(2))+sqrt(17-12*sqrt(2))等于多少上面的sqrt是根号的意思,求这道题怎么解,最后得数是1,
2*sqrt(3-2*sqrt(2))+sqrt(17-12*sqrt(2))等于多少
上面的sqrt是根号的意思,求这道题怎么解,最后得数是1,
2*sqrt(3-2*sqrt(2))+sqrt(17-12*sqrt(2))等于多少上面的sqrt是根号的意思,求这道题怎么解,最后得数是1,
sqrt(3-2*sqrt(2))
=sqrt(2-2*sqrt(2)+1)
=sqrt((sqrt(2)^2-2*sqrt(2)+1)
=sqrt((sqrt(2)-1)^2)
=sqrt(2)-1
同理,
sqrt(17-12*sqrt(2))
=sqrt(9-12*sqrt(2)+8)
=sqrt((3-sqrt(8))^2)
=3-2*sqrt(2)
所以,
2*sqrt(3-2*sqrt(2))+sqrt(17-12*sqrt(2))
=2(sqrt(2)-1)+3-2*sqrt(2)
=2*sqrt(2)-2+3-2*sqrt(2)
=1