根号计算

显示全部楼层 · 2019-8-17 17:39:27

已知a^(2/3)+b^(2/3)=4, x=a+3a^(1/3)b^(2/3), y=b+3a^(2/3)b^(1/3)
求(x+y)^(2/3)+(x-y)^(2/3)

千问 · 2019-8-17 17:39:27

开根号的计算方法...

千问 · 2019-8-17 17:39:27

显然，x+y=a+3a^(1/3)b^(2/3)+3a^(2/3)b^(1/3)+b=（a^(1/3)+b^(1/3))^3x-y=a+3a^(1/3)b^(2/3)-3a^(2/3)b^(1/3)-b=（a^(1/3)-b^(1/3))^3所以，(x+y)^(2/3)+(x-y)^(2/3)=（a^(1/3)+b^(1/3))^2+（a...

千问 · 2019-8-17 17:39:27

设a=8sinθ^3,b=8cosθ^3 代入，得x＝a＋3a^(1/3)·b^(2/3)=8sinθ^3+24sinθcosθ^2 y=8cosθ^3+24sinθ^2cosθ 则x+y =8sinθ^3+24sinθcosθ^2+8cosθ^3+24sinθ^2cosθ =8sinθ(sinθ^2+3cosθ^2)+8cosθ(cos...

千问 · 2019-8-17 17:39:27

x+y=a+3a^(2/3)b^(1/3)+3a^(1/3)b^(2/3)+b =(a^(1/3)+b^(1/3))^3x-y=a-3a^(2/3)b^(1/3)+3a^(1/3)b^(2/3)-b =(a^(1/3)-b^(1/3))^3(x+y)^(2/3)=(a^(1/3)+b^(1/3))^2(x-y)^(2/3)=(a^(1/3)-b^...

千问 · 2019-8-17 17:39:27

)=(a^(1/3)+b^(1/3))^2 (x-y)^(2/3)=(a^(1/3)-b^(1/3))^2 (x+y)^(2/3)+(x-y)^(2/3)=(a^(1/3)+b^(1/3))^2)+(a^(1/3)-b^(1/3))^2=2(a^(2/3)+b^(2/3))=8...