已知(x+y)²=4 (x-y)²=3则x²+y²
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/06 13:55:38
![已知(x+y)²=4 (x-y)²=3则x²+y²](/uploads/image/z/7617166-70-6.jpg?t=%E5%B7%B2%E7%9F%A5%28x%2By%29%26%23178%3B%3D4+%28x-y%29%26%23178%3B%3D3%E5%88%99x%26%23178%3B%2By%26%23178%3B)
已知(x+y)²=4 (x-y)²=3则x²+y²
已知(x+y)²=4 (x-y)²=3则x²+y²
已知(x+y)²=4 (x-y)²=3则x²+y²
x²+2xy+y²=4
x²-2xy+y²=3
相加x²+y²=7/2
(x+y)²=4
(x-y)²=3
展开得
2x^2+2y^2=7
x^2+y^2=7/2
x^2+2xy+y^2=4 x^2-2xy+y^2=3 两个相减:4xy=1,则xy=1/2,将它代入第一个式子:x^2+1/2+y^2=4,则x^2+y^2=7/3
(x+y)²=x²+y²+2xy
(x-y)²=x²+y²-2xy
(x+y)²-(x-y)²=4xy=1
由上式可得:2xy=0.5
x²+y²=(x+y)²-2xy=4-0.5=3.5
以后套公式就行了~顺便提一下变式【(x+y)²+(x-y)²=2x²+2y²】