Question

已知a、b为有理数,且(3-2乘根号3)^2=a+b乘根号3,求a+b的平方根

Answer 1

(3-2√3)^2=a+b√3

21-12√3=a+b√3

(a-21)+(b+12)√3=0

a-21=0 a=21

b+12=0 b=-12

±√(a+b)=±√(21-12)=±√9=±3