若x,y满足x²+y²=5/4,xy=-1/2,求下列各式的值:(1)(x+y)² (2)x^4+y^4 (3) x²-y²我最主要要第三个的
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/01 07:21:01
![若x,y满足x²+y²=5/4,xy=-1/2,求下列各式的值:(1)(x+y)² (2)x^4+y^4 (3) x²-y²我最主要要第三个的](/uploads/image/z/11675920-40-0.jpg?t=%E8%8B%A5x%2Cy%E6%BB%A1%E8%B6%B3x%26%23178%3B%2By%26%23178%3B%3D5%2F4%2Cxy%3D-1%2F2%2C%E6%B1%82%E4%B8%8B%E5%88%97%E5%90%84%E5%BC%8F%E7%9A%84%E5%80%BC%EF%BC%9A%EF%BC%881%EF%BC%89%EF%BC%88x%2By%EF%BC%89%26%23178%3B+%EF%BC%882%EF%BC%89x%5E4%2By%5E4+%EF%BC%883%EF%BC%89+x%26%23178%3B-y%26%23178%3B%E6%88%91%E6%9C%80%E4%B8%BB%E8%A6%81%E8%A6%81%E7%AC%AC%E4%B8%89%E4%B8%AA%E7%9A%84)
若x,y满足x²+y²=5/4,xy=-1/2,求下列各式的值:(1)(x+y)² (2)x^4+y^4 (3) x²-y²我最主要要第三个的
若x,y满足x²+y²=5/4,xy=-1/2,求下列各式的值:
(1)(x+y)² (2)x^4+y^4 (3) x²-y²
我最主要要第三个的
若x,y满足x²+y²=5/4,xy=-1/2,求下列各式的值:(1)(x+y)² (2)x^4+y^4 (3) x²-y²我最主要要第三个的
(1)原式=x²+y²+2xy
=5/4-1
=1/4;
(2)原式=(x²+y²)²-2x²y²
=25/16-2×(-1/2)²
=25/16-1/2
=17/16;
(3)(x-y)²=(x+y)²-4xy=1/4+2=9/4;
x-y=±3/2;
x+y=±1/2;
x²-y²=(x+y)(x-y)=±3/4;