Question

已知x=根号3+1,y=根号3-1,求下列各式的值 （1）x^2+2xy+y^2 (2)x^2-y^2

Answer 1

x^2+2xy+y^2 =(x+y)^2=(√3 +1 +√3 -1)^2=12

x^2-y^2=(x+y)(x-y)=(√3 +1 +√3 -1)(√3 +1 -√3 +1)=2√3 * 2=4√3