請幫我解題(算式) 1.化簡3根號5+1分之1為 2.設a-a分之1=3,則a的三方-a的三方之1之值為 3.化簡(2+根號5+根號6)(2-根號5+根號 6)= 4.已知f(x)各項係數和微20,且f(x)除以x+2所得商式為q(x),餘式為5,則q(x)除以x-1的餘式為?

1)
1/(3√5 + 1) = (3√5 - 1) / ((3√5 + 1)(3√5 - 1)) = (3√5 - 1) / (45 - 1) = (3√5 - 1) / 44.

2)
a - 1/a = 3
(a - 1/a)³ = 27
a³ - 3a + 3/a - 1/a³ = 27
a³ - 1/a³ = 27 + 3(a - 1/a)
a³ - 1/a³ = 27 + 3(3)
a³ - 1/a³ = 36

3)
(2 + √5 + √6)(2 - √5 + √6)
= (2+√6 + √5)(2+√6 - √5)
= (2 + √6)² - 5
= 4 + 4√6 + 6 - 5
= 5 + 4√6

4)
各項係數和 = f(1) = 20,
f(x) = q(x) (x+2) + 5
f(1) = q(1) (3) + 5
20 = 3q(1) + 5
q(1) = 5
∴ q(x) 除以 x - 1 的餘式為 5.