初中数学整式运算1.已知a+b=1,a^2+b^2=2,求a^5+b^5的值,2.计算(a+1)^2(a-1)^23.观察一组式子,3^2+4^2=5^2,5^2+12^2=13^2,7^2+24^2=25^2,猜想一下,第n个式子是.要完整的过程.谢谢
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![初中数学整式运算1.已知a+b=1,a^2+b^2=2,求a^5+b^5的值,2.计算(a+1)^2(a-1)^23.观察一组式子,3^2+4^2=5^2,5^2+12^2=13^2,7^2+24^2=25^2,猜想一下,第n个式子是.要完整的过程.谢谢](/uploads/image/z/6867735-15-5.jpg?t=%E5%88%9D%E4%B8%AD%E6%95%B0%E5%AD%A6%E6%95%B4%E5%BC%8F%E8%BF%90%E7%AE%971.%E5%B7%B2%E7%9F%A5a%2Bb%3D1%2Ca%5E2%2Bb%5E2%3D2%2C%E6%B1%82a%5E5%2Bb%5E5%E7%9A%84%E5%80%BC%2C2.%E8%AE%A1%E7%AE%97%28a%2B1%29%5E2%28a-1%29%5E23.%E8%A7%82%E5%AF%9F%E4%B8%80%E7%BB%84%E5%BC%8F%E5%AD%90%2C3%5E2%2B4%5E2%3D5%5E2%2C5%5E2%2B12%5E2%3D13%5E2%2C7%5E2%2B24%5E2%3D25%5E2%2C%E7%8C%9C%E6%83%B3%E4%B8%80%E4%B8%8B%2C%E7%AC%ACn%E4%B8%AA%E5%BC%8F%E5%AD%90%E6%98%AF.%E8%A6%81%E5%AE%8C%E6%95%B4%E7%9A%84%E8%BF%87%E7%A8%8B.%E8%B0%A2%E8%B0%A2)
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初中数学整式运算1.已知a+b=1,a^2+b^2=2,求a^5+b^5的值,2.计算(a+1)^2(a-1)^23.观察一组式子,3^2+4^2=5^2,5^2+12^2=13^2,7^2+24^2=25^2,猜想一下,第n个式子是.要完整的过程.谢谢
初中数学整式运算
1.已知a+b=1,a^2+b^2=2,求a^5+b^5的值,
2.计算(a+1)^2(a-1)^2
3.观察一组式子,3^2+4^2=5^2,5^2+12^2=13^2,7^2+24^2=25^2,猜想一下,第n个式子是.
要完整的过程.谢谢
初中数学整式运算1.已知a+b=1,a^2+b^2=2,求a^5+b^5的值,2.计算(a+1)^2(a-1)^23.观察一组式子,3^2+4^2=5^2,5^2+12^2=13^2,7^2+24^2=25^2,猜想一下,第n个式子是.要完整的过程.谢谢
1.a+b=1
两边平方
a^2+b^2+2ab=1
所以ab=[1-(a^2+b^2)]/2=-1/2
a^3+b^3=(a+b)(a^2+b^2-ab)=1*(2+1/2)=5/2
a^5+b^5
=(a^2+b^2)(a^3+b^3)-a^2b^3-a^3b^2
=(a^2+b^2)(a^3+b^3)-(ab)^2(a+b)
=2*(5/2)-(-1/2)^2*1
=19/4
2.a^4-2a^2+1
3.(2n+1)^2+(n(2n+1)+n)^2
=(n(2n+1)+n+1)^2