X加Y等于1 X的平方加Y的平方等于2求 X的7次方加上Y的7次方
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x+y=1
x^2+y^2=2
(x+y)^2=x^2+y^2+2xy=1^2=1
所以2xy=1-2
xy=-1/2
x^3+y^3=(x+y)(x^2-xy+y^2)=1*[2-(-1/2)]=5/2
(x^2+y^2)^2=x^4+y^4+2(xy)^2=2^2=4
x^4+y^4=4-2(xy)^2=4-2/4=7/2
x^7+y^7
=(x^3+y^3)(x^4+y^4)-x^3y^4-x^4y^3
=(5/2)*(7/2)-(xy)^3*y-(xy)^3*x
=35/4-y*(-1/2)^3-x*(-1/2)^3
=35/4+y/8+x/8
=35/4+(x+y)/8
=35/4+1/8
=71/8
x^2+y^2=2
(x+y)^2=x^2+y^2+2xy=1^2=1
所以2xy=1-2
xy=-1/2
x^3+y^3=(x+y)(x^2-xy+y^2)=1*[2-(-1/2)]=5/2
(x^2+y^2)^2=x^4+y^4+2(xy)^2=2^2=4
x^4+y^4=4-2(xy)^2=4-2/4=7/2
x^7+y^7
=(x^3+y^3)(x^4+y^4)-x^3y^4-x^4y^3
=(5/2)*(7/2)-(xy)^3*y-(xy)^3*x
=35/4-y*(-1/2)^3-x*(-1/2)^3
=35/4+y/8+x/8
=35/4+(x+y)/8
=35/4+1/8
=71/8
参考资料: http://zhidao.baidu.com/question/49143833.html
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