solving equations invovling radicals?

Question

equation:
sqrt (2x-4) + 2 = sqrt (3x+4)

do i need to square both equations then move the 2 or vice versa?

equation:
2x^2 + 1 = 1- x

do i need to move the one over then square the equation or vice versa?

thanks.

Answer 1

squaring both sides
2x-4+4+4rt(2x-4)=3x+4
-x-4=4rt(2x-4)
x^2+8x+16=16(2x-4)
x^2-24x+80=0
(x-20)(x-4)=0
x=20 or 4

Answer 2

Note: When solving equations by squaring both sides it sometimes happens that you introduce a redundant root, and it is advisable to check the solutions in the original equation to rule out this possibility.

Answer 3

sqrt (2x-4) + 2 = sqrt (3x+4)
if you square both:
2x-4 +4 sqrt (2x-4) +4 =3x+4
simplify
4 sqrt (2x-4) =x+4
sqrt (2x-4) = (x+4)/4
square again:
2x-4= (x+4)^2 /16
16 (2x-4)= (x+4)^2
32 x - 64 = x^2 + 8x +16
x^2 - 24 x + 80 =0
(x-20)(x-4)=0
x=20 or 4

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