很难的【因式分解】：3x^2+4xy-y^2=3(x-((2+√7)/3)y))(x-((2-√7)/3)y))_数学解答

很难的【因式分解】：3x^2+4xy-y^2
=3(x-((2+√7)/3)y))(x-((2-√7)/3)y))

人气：307 ℃　时间：2020-10-02 00:17:41

解答

3x^2+4xy-y^2 = 3(x^2+ xy*4/3 - y^2*1/3) = 3[(x^2+ 2*2/3 *xy +4/9y^2) - y^2/3- 4/9y^2] = 3[(x+2/3y)^2 - 7/9 y^2]
=3(x+2/3y +√7/3y)(x+2/3y - √7/3y) = 3[x+(2+√7)/3y][x+(2-√7)/3y]