1.
√2x-4-√x+5=1
√2x-4=1+√x+5
(√2x-4)^2=(1+√x+5)^2
2x-4=1+2√x+5+x+5
2x-4=2√x+5+x+6
2x-4-x-6=2√x+5
x-10=2√x+5
(x-10)^2=(2√x+5)^2
x^2-20x+100=4(x+5)
x^2-20x+100=4x+20
x^2-20x+100-4x-20=0
x^2-24x+80=0
(x-20)(x-4)=0
x1=20,x2=4
经检验x=4是增根,x=20是方程的解.
2.
x^2+√x^2-1=3
根据换元法得:x^2=a
a+√a-1-3=0
a-3=√a-1
(a-3)^2=(√a-1)^2
a^2-6a+9=a-1
a^2-6a+9-a+1=0
a^2-7a+10=0
(a-2)(a-5)=0
a1=2,a2=5
即:
x^2=2,x^2=5
x1=√2,x2=-√2,x3=√5,x4=-√5
经检验x3=√5,x4=-√5是增根,x1=√2,x2=-√2是方程的解.