Question Number 10212 by konen last updated on 30/Jan/17

x+y=12  x×y=16  ⇒(√(x/y))−(√(y/x)) =?

Answered by ridwan balatif last updated on 30/Jan/17

x+y=12→x=12−y...(∗)  xy=16→(12−y)y=16  −y^2 +12y=16  y^2 −12y+16=0  y_(1,2) =((−(−12)±(√((−12)^2 −4×1×16)))/(2×1))  y_(1,2) =((12±4(√5))/2)  y_(1,2) =6±2(√5)  y_1 =6+2(√5)→x_1 =6−2(√5)  y_2 =6−2(√5)→x_2 =6+2(√5)  ((√x)/(√y))−((√y)/(√x))=((x−y)/(√(xy)))=((x−y)/4), xy=16→(√(xy))=4  for x_1 &y_1 ,then  ((x_1 −y_1 )/4)=(((6−2(√5))−(6+2(√5)))/4)=−(√5)  for x_2 &y_2 ,then  ((x_2 −y_2 )/4)=(((6+2(√5))−(6−2(√5)))/4)=(√5)

Answered by nume1114 last updated on 30/Jan/17

    (x−y)^2   =(x+y)^2 −4xy  =12^2 −4∙16  =80  ⇒x−y=±(√(80))=±4(√5)      (√(x/y))−(√(y/x))  =((√x)/(√y))−((√y)/(√x))  =((x−y)/(√(xy)))  =((±4(√5))/(√(16)))=±(√5)

Answered by arge last updated on 04/Feb/17

    x+y=12....(i)  xy=16.......(ii)    y=((16)/x)    x+((16)/x)=12    ((x^2 +16)/x)=12    x^2 =12x+16=0  x_1 =10.47  x_2 =1.53  y_1 =1.53  y_2 =10.47    (√((10.47)/(1.53))) =(√((1.53)/(10.47))) = 2.24 ∴∴∵Rta