MATHS F.4......THX!!!

37
x－5√x+4=0
Set y=√x
y^2－5y+4=0
(y－1)(y－4)=0
y=1 or y=4
√x=1 or √x=4
x=1or x=16

38
x^4－29x^2+100=0
(x^2－25)(x^2－4)=0
x^2=25 or x^2=4
x=+/-5or x=+/-2

39
(5^(2x)－-125)^2=0
5^(2x)－-125=0
5^(2x)=125
2x=3
x=3/2

44
√(x^2+27)=x^2－3
Set y=x^2+27
x^2=y－27
√y=y－27－3
y=y^2－60y+900
y^2－61y+900=0
(y－25)(y－36)=0
y=25 or y=36
x^2+27=25(reject) or x^2+27=36
x^2=9
x=+/-3

45 x=2√(x－3)+6
Sol
Set y=√(x－3)
y^2=x－3
x=y^2+3
y^2+3=2y+6
y^2－2y－3=0
(y－3)(y+1)=0
y=3 or y=－1(reject)
x=9+3=12

46
(x+1/x)^2=4
x^2+2+1/x^2=4
x^4+2x^2+1=4x^2
x^4-2x^2+1=0
(x^2－1)^2=0
x^2－1=0
x=+/-1

47
(5^x)－5(5^2)=－4
Set y=5^(x)
y^2－125=－4
y^2－121=0
(y－11)(y+11)=0
y=11 or y=－11(reject)
5^(x)=11
xlog5=log11
x=log5_11

48.
5^(2x)+30*(5^x)+125=0
Set y=5^(x)
y^2+30y+125=0
(y+5)(y+25)=0
y=－5 or y=－25
5^(x)=－5 or 5^(x)=－25
x=－1 or x=－2