Question

x+y=m， x^3+y^3=n ，m不等于0求x^2+y^2

Answer 1

(x+y)²=m²
x²+y²+2xy=m²
令a=x²+y²,b=xy
则a+2b=m² (1)

x²+y³=(x+y)(x²-xy+y²)=n
m(a-b)=n
a-b=n/m (2)
(1)+(2)×2
a+2a=m²+2n/m=(m³+2n)/m
所以x²+y²=a=(m³+2n)/(3m)

Answer 2

x+y=m， x^3+y^3=n ，m不等于0;
x^2+y^2+2xy=m^2 (1)
x^2+y^2-xy=n/m (2)
[(1)+2*(2)]/3
x^2+y^2=(m^2+2n/m)/3 =(m^3+2n)/3m

Answer 3

解：①²，得：x²+y²+2xy = m² ③
②：（x+y)(x²+y²-xy）=n
x²+y² -xy = n/m ④
④×2 + ③，得：
3（x² +y²）= m² +2n/m
故：x²+y² = m²/3 +2n/(3m)
= (m³ +2n) / (3m)