Question

解方程：x的平方-根号(x的平方-3x+5)=3x+1

Answer 1

x²-√(x²-3x+5)=3x+1

(x²-3x+5)-6=√(x²-3x+5)

令t=√(x²-3x+5) 代入 (t>0)

则t²-6=t

(t-3)(t+2)=0

得t=3 or -2(舍去)

所以√(x²-3x+5)=3

x²-3x+5=9

x²-3x-4=0

(x-4)(x+1)=0

解得x=4 or -1