Question

若已知x+y=1,x^2+y^2=2,求x^4+y^4和x^4-y^4的值

如题！！！！在线等！！！谢谢
大哥大姐们～我说这是初一下学期的题，请不要在答案里有什么“√”这个东西耶

Answer 1

(x+y)^2=x^2+y^2+2xy=1 (x-y)^2=x^2+y^2-2xy=2+1=3 x-y=±√3
2xy=-1 xy=-1/2 x^2y^2=1/4
(x^2+y^2)^2=x^4+y^4+2x^2y^2=4
x^4+y^4=4-2x^2y^2=4-1/2=7/2
x^4-y^4=(x^2+y^2)(x^2-y^2）=(x^2+y^2)(x+y)(x-y)=2*1*√3 =±2√3
肯定要有的,如果不要根号3就取近似值1.732代入吧

Answer 2

x+y=1
平方得：
x²+y²+2xy=1
2+2xy=1
xy=-1/2
x²y²=1/4
(x-y)²=x²+y²-2xy=2+1=3
x-y=±√3

x^4+y^4=(x²+y²)²-2x²y²=4-2×1/4=7/2
x^4-y^4=(x²+y²)(x²-y²)=(x²+y²)(x+y)(x-y)=2×1×(±√3)=±2√3

Answer 3

(x+y)^2=x^2+y^2+2xy=1
2+2xy=1
xy=-1/2
(x-y)^2=x^2+y^2-2xy=2-2*(-1/2)=3
x-y=±√3
x^4+y^4=(x^2+y^2)^2-2x^2y^2=2^2-2*(-1/2)^2=7/2
x^4-y^4=(x^2+y^2)(x^2-y^2)=(x^2+y^2)(x+y)(x-y)=2*1*±√3=±2√3
补充：√是根号，√3 就是根号3

Answer 4

x+y=1
x^2+y^2=2
xy=[(x+y)²-(x^2+y^2)]/2=(1-2)/2=-1/2
所以
x-y=±√[x^2+y^2-2xy]=±√(2+1)=±√3
x^4+y^4=(x^2+y^2)^2-2x^2y^2=4-2*(1/4)=7/2

x^4-y^4=(x^2+y^2)(x^2-y^2)=2*(x-y)(x+y)=2*(±√3)=±2√3

Answer 5

由x²+y²=(x+y)²-2xy可解xy=-1/2
由x²+y²=(x-y)²+2xy可解x-y=√3或-√3
∴x^4+y^4=(x²+y²)²-2x²y²=7/2
x^4-y^4=(x²+y²)(x²-y²)=(x²+y²)(x+y)(x-y)=2√3或-2√3