Question

已知x=1/√5-√3,y=1/√5+√3,利用x+y,x-y,xy等代数式的值,求x²-3xy+y²

Answer 1

x+y = 2/(√5+√3)=2(√5-√3)/(5-3) = √5 - √3xy = 1/(√5+√3)^2=1/(8+2√15)=1/[2(4+√15)] = (4-√15)/2=2-0.5√15x^2+y^2=(x+y)^2-2xy=(√5-√3)^2-(4-√15)=(8-2√15)-4+√15 =4-√15x-y=-2√3x/y-y/x=(x^2-y^2)/(xy)=-2√3(√5 - √3)/(2-0.5√15)亲 这里你自己化简一下哦x^2+y^2-3xy=4-√15-6+3√15 =2√15-2