已知x=2+根号3,y=2-根号3,计算代数式(x+y/x-y-x-y/x+y)乘以(1/x^2-1/y^2)
2019-05-07
已知x=2+根号3,y=2-根号3,计算代数式(x+y/x-y-x-y/x+y)乘以(1/x^2-1/y^2)
优质解答
即xy=2²-(√3)
=4-3=1
原式=[(x+y)²-(x-y)²]/(x+y)(x-y)*[-(x²-y²)/x²y²]
=(x²+2xy+y²-x²+2xy-y²)/(x+y)(x-y)*[-(x²-y²)/x²y²]
=-4xy/(x²-y²)*(x²-y²)/x²y²
=-4/xy
=-4/1
=-4
即xy=2²-(√3)
=4-3=1
原式=[(x+y)²-(x-y)²]/(x+y)(x-y)*[-(x²-y²)/x²y²]
=(x²+2xy+y²-x²+2xy-y²)/(x+y)(x-y)*[-(x²-y²)/x²y²]
=-4xy/(x²-y²)*(x²-y²)/x²y²
=-4/xy
=-4/1
=-4