根号6+根号5的和的六次方取整

解：设 x= √6 +√5,
y= √6 -√5,
则 x^2 +y^2 =22,
x^2 y^2 =1.
所以 x^6 +y^6 = (x^2 +y^2) (x^4 -x^2 y^2 +y^4)
= (x^2 +y^2) [ (x^2 +y^2)^2 -3 x^2 y^2]
= 22 *(22^2 -3*1)
=10582.
又因为 0 所以 0 所以 10581 即 (√6 +√5)^6 取整为 10581.

= = = = = = = = =
x^6 -y^6 = (x^2 -y^2) (x^4 +x^2 y^2 +y^4)
= (x^2 -y^2) [ (x^2 +y^2)^2 -x^2 y^2) ]
= 4√30 (22^2 -1)
≈10581.

但这个要用计算器。

百度一下：
((6^(1/2))+(5^(1/2)))^6 = 10 581.9999055

10552.80……取整就是10552