Question

用配方法解方程：y^2+2(根号3+1）y+2根号2=0

用配方法解方程：y^2+2(根号3+1）y+2根号2=0

Answer 1

y^2+2(√3+1)y=-2√2
y^2+2(√3+1)y+(√3+1)^2=-2√2+(√3+1)^2
(y+√3+1)^2=-2√2+4+2√3
y+√3+1=±√(-2√2+4+2√3)
所以y1=-√3-1+√(-2√2+4+2√3)
y2=-√3-1-√(-2√2+4+2√3)

Answer 2

y^2+2(根号3+1）y+2根号2=0
y^2+2(根号3+1）y+(根号3+1）^2=(根号3+1）^2-2√2
(y+√3+1)^2=4+2√3-2√2
y=±√(4+2√3-2√2)-(√3+1)