∵(x-y)^2=(-4)^2.

x^2-2xy+y^2= 16.

(x^2-2xy+y^2)/2= 16/2

∴(x^2+y2)/2-xy=8.

2. If x 2-4x+ 1 = 0.

Q: (1)x+ 1/x=? ②x^2+ 1/x^2=？ (3)x- 1/x=？ (4)x^4+ 1/x^4=？

Solution: x = 2 √ 3 from x 2-4x+ 1 = 0.

( 1)x+ 1/x =(2√3)+ 1/(2√3)，

After rationalizing the denominator, we get:

x+ 1/x=4。

(2)x^2+ 1/x^2=(2 √3)^2+ 1/(2 √3)^2

= (7+4 √ 3)+ 1/(7+4 √ 3), after physicochemical and sequencing, it is obtained:

x^2+ 1/x^2= 14.

(3) x-1/x = 2 √ 3-1/(2 √ 3), which is simplified as above:

x- 1/x= 2√3。

(4)x^4+ 1/x^4=(x^2+ 1/x^2)^2-2= 14^2-2= 196-2= 194.

X 2+ 1/x 2 = 14 See (2).

In the process of solving problems, the complete square formula is used:

(a+b)^2=a^2+2ab+b^2，

(a-b)^2=a^2-2ab+b^2.