Given x (x-1) - (X & # 178; y) = - 2, find the value of X & # 178; + Y & # 178 / 2-xy As above

Given x (x-1) - (X & # 178; y) = - 2, find the value of X & # 178; + Y & # 178 / 2-xy As above

X (x-1) - (X & # 178; y) = - 2
x²-x-x²+y=-2
∴-x+y=-2
That is, X-Y = 2
(x²+y²)/2-xy
=1/2(x²+y²-2xy)
=1/2(x-y)²
=2²÷2
=2

Given X-Y = 2, xy = 1, find the value of X & # 178; (X-Y) - Y & # 178; (Y-X)

x-y=2 (x-y)²=x²-2xy+y²=4
xy=1 2xy=2
x²+y²=6
x²（x-y）-y²（y-x）
=x²（x-y）+y²（x-y）
=(x²+y²)（x-y）=2*6=12

If x + y = 4, xy = 1, then x & # 178; + Y & # 178=___ process

Solution
x+y=4
The square of both sides is as follows:
(x+y)²=16
That is, X & # 178; + 2XY + Y & # 178; = 16
That is, X & # 178; + Y & # 178; + 2 = 16
x²+y²=14