Question

在实数范围内分解因式 3x^2+4xy-y^2

Answer 1

3x²+4xy-y²
=3(x²+ xy×4/3 - y²×1/3)
=3[(x²+ 2×2/3 ×xy +4/9y²) - y²/3- 4/9y²]
=3[(x+2/3y)² - 7/9 y²]
=3(x+2/3y +√7/3y)(x+2/3y - √7/3y)
=3[x+(2+√7)/3y][x+(2-√7)/3y]

Answer 2

3x^2+4xy-y^2
=3(x^2+4xy/3+4/9y^2)-7y^2/3
=3(x+2/3y)^2-7y^2/3
=[根号3(x+2/3y)+根号(7/3)y][根号3(x+2/3y)-根号(7/3) y]
=(根号3 x+(2根号3+根号21)/3 y)(根号3 x+(2根号3-根号21)/3 y)