Question

x^2-根号下(x^2-3x+5)=3x+1

要详细过程 急求

Answer 1

x²-3x+5-√(x²-3x+5)-6=0
设y=√(x²-3x+5)
∴y²-y-6=0
y=3或y=-2(舍去)
∴√(x²-3x+5)=3
∴x²-3x+5=9
x²-3x-4=0
x=4或x=-1
检验：x=4或x=-1是方程的根
∴方程的根是x=4或x=-1

Answer 2

x^2-√(x^2-3x+5)=3x+1
x^2-3x+5-√(x^2-3x+5)-6=0
(√(x^2-3x+5)^2-√(x^2-3x+5)-6=0
(√(x^2-3x+5)-3)(√(x^2-3x+5)+2)=0
√(x^2-3x+5)-3=0
√(x^2-3x+5)=3
x^2-3x+5=9
x^2-3x-4=0
(x-4)(x+1)=0
x1=4 x2=-1