化简(√2+√3+√5)²+(√2+√3-√5)²+(√2-√3+√5)²+(-√2+√3+√5)²
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/20 04:21:03
![化简(√2+√3+√5)²+(√2+√3-√5)²+(√2-√3+√5)²+(-√2+√3+√5)²](/uploads/image/z/7107265-1-5.jpg?t=%E5%8C%96%E7%AE%80%28%E2%88%9A2%2B%E2%88%9A3%2B%E2%88%9A5%29%26%23178%3B%2B%28%E2%88%9A2%2B%E2%88%9A3-%E2%88%9A5%29%26%23178%3B%2B%28%E2%88%9A2-%E2%88%9A3%2B%E2%88%9A5%29%26%23178%3B%2B%28-%E2%88%9A2%2B%E2%88%9A3%2B%E2%88%9A5%29%26%23178%3B)
x){3G10TS64FbbjMR>=/~>醍ϛE^Wn76 3iz~OG"{:6t10U m5J*06@JA@B uiuiCt&; µh[
t)\TYOvndz9foܓ}jy6mSuouT'$ف \,
化简(√2+√3+√5)²+(√2+√3-√5)²+(√2-√3+√5)²+(-√2+√3+√5)²
化简(√2+√3+√5)²+(√2+√3-√5)²+(√2-√3+√5)²+(-√2+√3+√5)²
化简(√2+√3+√5)²+(√2+√3-√5)²+(√2-√3+√5)²+(-√2+√3+√5)²
.看着就烦
设√2+√3=a,√2-√3=b
则原式可化为(a+√5)²+(a-√5)²+(b+√5)²+(b+√5)²
=2a²+5+2(b²+2√5b+5)
=2a²+2b²+4√5b+15
=2(2+3+2√6)+2(2+3-2√6)+4√5(√2-√3)+15
=20+8√10-8√15+15
=35+√10-8√15
.也许有更简便的方法,直接计算也可以