Question

已知a=根号3+1,求（a+1/a）的平方-4（a+1/a）+4的值

Answer 1

(a + 1/a)² - 4(a + 1/a) + 4

= (a + 1/a - 2)²

= [√3 + 1 + (√3 - 1)/2 - 2]²

= (3√3/2 - 3/2)²

= 27/4 + 9/4 - 9√3/2

= 9 - 9√3/2