初二数学(30)
已知实数x,y满足(x平方)+(根号2)y=(根号3),(y平方)+(根号2)x=(根号3),且x≠y,则(y/x)+(x / y)等于多少?
x^2+(√2)y=√3---------(1) y^2+(√2)x=√3---------(2) (1)-(2) x^2-y^2-(√2)(x-y)=0 (x-y)(x+y-√2)=0----(x≠y) x+y=√2代入(1)(2)得 x^2+(√2)(√2-x)=√3 x^2-√2x+2-√3=0 y^2-√2y+2-√3=0 设x,y是方程z^-√2z+2-√3=0的两个根,有 x+y=√2 xy=2-√3 y/x+x/y=(y^2+x^2)/xy =[(x+y)^2-2xy]/xy =[2-2(2-√3)]/(2-√3) =2√3+2
过程很难打出来..直接说答案吧!!! 根号3/2-根号3
答:(x+y+1)^2 =x^2+y^2+2xy+2x+2y+1 =(x^2+y^2)+2(x+xy+y+1)+1 =6+4+6根号2+1=11+6根号2=(3+根...详情>>
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