Question

已知x=√5+√7,y=√7-√5,求x^2-xy+y^2的值

Answer 1

因为x=√5+√7,y=√7-√5,所以：

x^2-xy+y^2=(x+y)^2-3xy=(2√7)^2-3(√5+√7)(√7-√5)=28-3(7-5)=22