Question

已知x^2-xy=4,xy+y^2 = -3,求下列各式的值

1. x^2+y^2
2. x^2+2xy+3y^2
3. 2x^2-xy+y^2

Answer 1

x²＋y²=(x²－xy)＋(xy＋y²)=4＋(－3)=1；
x²＋2xy＋3y²=(x²－xy)＋3(xy＋y²)=4＋3×(－3)=－5；
2x²－xy＋y²=2(x²－xy)＋(xy＋y²)=2×4－3=5

Answer 2

1 5 5

Answer 3

1. x^2+y^2= x^2-xy+xy+y^2=4-3=1
2. x^2+2xy+3y^2=x^2-xy+3xy+3y^2=4-9=-5
3. 2x^2-xy+y^2=2x^2-2xy+xy+y^2=8-3=5

Answer 4

设 x^2-xy=4,xy+y^2 = -3
分别为 (1)式 (2)式
1 将两式相加，就能得到
x^2+y^2 = 1
2 (1)式+(2)式*3，就得到
x^2+2xy+3y^2 = -5
3 (1)式*2+(2)式，就能得到
2x^2-xy+y^2 = 5

Answer 5

答案分别是：
1 （两个式子直接加起来）
-5 等于 x^2-xy + 3(y^2+xy)
5 等于 x^2+y^2 +x^2-xy

Answer 6

1. x^2+y^2= (x^2-xy)+(xy+y^2）=4-3=1
2. x^2+2xy+3y^2=（x^2-xy）+3（xy+y^2）=4+3*（-3）=-5
3. 2x^2-xy+y^2=2（x^2-xy）+（xy+y^2）=2*4-3=5