一道超难的数学题若xy=1/2,求代数式3(x+y)^2÷3(x-y)^2的值
2019-05-07
一道超难的数学题
若xy=1/2,求代数式3(x+y)^2÷3(x-y)^2的值
优质解答
3(x+y)^2÷3(x-y)^2
X^2+Y^2+2XY
__________________
X^2+Y^2-2XY
=(x+y)^2÷(x-y)^2
={(X+Y)÷(X-Y)}^2
={(X-Y+2Y)÷(X-Y)}^2
=(1+2Y/X-Y)^2
3(x+y)^2÷3(x-y)^2
X^2+Y^2+2XY
__________________
X^2+Y^2-2XY
=(x+y)^2÷(x-y)^2
={(X+Y)÷(X-Y)}^2
={(X-Y+2Y)÷(X-Y)}^2
=(1+2Y/X-Y)^2