根据题目条件的信息,选用恰当的化简技巧,是解决课本二次根式题的关键.一、变换所求,以简驭繁例1已知x=1/2(7~(1/2)+5~(1/2)),y=1/2(7~(1/2)-5~(1/2)),求x2-xy+y2的值.解当x=1/2(7~(1/2)+5~(1/2)),y=1/2(7~(1/2)-5~(1/2))时,有x-y=5~(1/2),xy=1/2.∴原式=(x-y)2+xy=(5~(1/2))2+1/2=11/2.二、化简变形,化难为易例2已知x=(3~(1/2)+2)/(3~(1/2)-2),y=(3~(1/2)-2)/(3~(1/2)+2),求 According to the information of the topic conditions, the selection of appropriate simplification skills is the key to solve the secondary root problems of the textbook. First, the transformation requires, to simplify the traditional example 1 known x = 1/2 (7 ~ (1/2) +5~(1/2)), y=1/2(7~(1/2)-5~(1/2)), find the value of x2-xy+y2. When the solution is x=1/2( When 7~(1/2)+5~(1/2)),y=1/2(7~(1/2)-5~(1/2)), there is xy=5~(1/2) ), xy = 1/2. ∴ original formula = (xy) 2+xy = (5 ~ (1/2)) 2+ 1/2 = 11/2. Second, Simplify the deformation, the difficulty is easy Example 2 has been Know x=(3~(1/2)+2)/(3~(1/2)-2), y=(3~(1/2)-2)/(3~(1/2)+ 2), seeking