问题
填空题
已知:x+y=10,x3+y3=400,则x2+y2=______.
答案
∵x3+y3=(x+y)(x2-xy+y2)
=10(x2+y2-xy)=400
x2+y2-xy=40…①
x+y=10 平方,
x2+2xy+y2=100…②
①×2+②得:2x2+2y2+x2+y2=80+100,
3(x2+y2)=180,
x2+y2=60,
故答案为60.
已知:x+y=10,x3+y3=400,则x2+y2=______.
∵x3+y3=(x+y)(x2-xy+y2)
=10(x2+y2-xy)=400
x2+y2-xy=40…①
x+y=10 平方,
x2+2xy+y2=100…②
①×2+②得:2x2+2y2+x2+y2=80+100,
3(x2+y2)=180,
x2+y2=60,
故答案为60.