已知a²-b²=1+根号2,b²-c²=1-根号2,则a四次方+b四次方+c四次方-a²b²-b²c²-a²c²=?
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 01:36:33
![已知a²-b²=1+根号2,b²-c²=1-根号2,则a四次方+b四次方+c四次方-a²b²-b²c²-a²c²=?](/uploads/image/z/8652651-51-1.jpg?t=%E5%B7%B2%E7%9F%A5a%26%23178%3B-b%26%23178%3B%3D1%2B%E6%A0%B9%E5%8F%B72%2Cb%26%23178%3B-c%26%23178%3B%3D1-%E6%A0%B9%E5%8F%B72%2C%E5%88%99a%E5%9B%9B%E6%AC%A1%E6%96%B9%2Bb%E5%9B%9B%E6%AC%A1%E6%96%B9%2Bc%E5%9B%9B%E6%AC%A1%E6%96%B9-a%26%23178%3Bb%26%23178%3B-b%26%23178%3Bc%26%23178%3B-a%26%23178%3Bc%26%23178%3B%3D%3F)
已知a²-b²=1+根号2,b²-c²=1-根号2,则a四次方+b四次方+c四次方-a²b²-b²c²-a²c²=?
已知a²-b²=1+根号2,b²-c²=1-根号2,
则a四次方+b四次方+c四次方-a²b²-b²c²-a²c²=?
已知a²-b²=1+根号2,b²-c²=1-根号2,则a四次方+b四次方+c四次方-a²b²-b²c²-a²c²=?
a-b=1+根号2,b-c=1-根号2
a-c=2
所以
a²+b²+c²-ab-bc-ac
=1/2(2a²+2b²+2c²-2ab-2bc-2ac)
=1/2[(a-b)²+(b-c)²+(c-a)²]
=1/2[(1+根号2)²+(1-根号2)²+(-2)²]
=1/2[3+2根号2+3-2根号2+4]
=1/2×10
=5