x^2 + (根号2）y = (根号3），y^2 + (根号2）x = (根号3）。且x不等于y, 求 (y/x)+ (x/y).
热心网友
x^2+根号2*y=根号3 (1),y^2+根号2*x=根号3 (2),(1)-(2)化简得x+y=根号2 (3),(1)+(2)变形:(x+y)^2-2xy+根号2(x+y)=2根号3 (4),把(3)代入(4)得xy=2-根号3.(y/x)+(x/y)=(x+y)^2/xy-2=2+2根号3
热心网友
x^2+2^0.5*y=3^0.5-----(1) y^2+2^0.5*x=3^0.5-----(2) (1)-(2): x^2-Y^2=2^0.5(x-y) x+y=2^0.5 (1)+(2): x^2+y^2+2^0.5(x+y)=2*3^0.5 x^2+y^=2(3^0.5-1) xy=0.5*[(x+y)^2-(x^2+y^2)] =2-3^0.5 x/y+y/x=(x^2+y^2)/(x*y) =2*(3^0.5-1)/(2-3^0.5) =2+2*3^(1/2)
热心网友
x^2 + (根号2)y = (根号3）---------(1)y^2 + (根号2)x = (根号3）---------(2)由(1)-(2)得：(x^2-y^2)+((根号2)y-(根号2)x)=0→(x-y)(x+y-(根号2))=0由于x不等于y, 故x+y-(根号2)=0,即得：x+y=根号2---------(3)由(1)+(2)得：(x^2+y^2)+((根号2)y+(根号2)x)=2(根号3)→((x+y)^2-2xy)+(根号2)(x+y)=2(根号3)代入(3)式得：2-2xy+2=2(根号3)故：xy=2-根号3 ---------(4)得：x^2+y^2=(x+y)^2-2xy=4-2(2-根号3)=2*根号3所以(y/x)+ (x/y)=(x^2+y^2)/xy=2*根号3/(2-根号3)=2*根号3(2+根号3)=6+4*根号3。
热心网友
x^2 + (根号2）y = (根号3）---------(1)y^2 + (根号2）x = (根号3）---------(2)(1)-(2)有：x^2-y^2=根号2（x-y)因为x不等于y所以x+y=根号2--------(3)(1)+(2)有：x^2 + y^2 + (根号2）(x +y)=2根号3配方得（x+ y）^2 + (根号2）(x +y)-2xy=2根号3---------(4)把（3）代入（4）得xy=2-根号3故(y/x)+ (x/y)=(x^2 + y^2)/xy=(（x+ y）^2-2xy)/xy=3+2根号3