Question

已知x+y=a,x²+y²=b,求4x²y²

Answer 1

（x+y）²=x²+y²+2xy=a²，x²+y²=b
2xy=a²-b
4x²y² =（2xy）²=（a²-b)²=a^4+b²-2a²b

Answer 2

4x²y² =（2xy）²=（（x+y）²-x-y）²
=（a²-b）²
=a^4-2a²b+b²

Answer 3

x+y＝a
（x＋y）²＝a²
x²＋y²＋2xy=a²
b+2xy=a²
2xy=a²－b
（2xy）²＝（a²－b）²
4x²y² ＝（a²－b）²＝a∧4＋b²-2a²b

Answer 4

a的平方减b.

Answer 5

(x+y)²=x²+y²+2xy=b+2xy
b+2xy=a²
xy=a²-b/2
4x²y² =(a²-b)²

Answer 6

(x+y)²=x²+y²+2xy
2xy=(x+y)²-x²+y²=a²-b

4x²y²=(2xy)²=(a²-b)²