Question

sqrt (x-2) + sqrt (x+2)=4
i have no idea how to get rid of the surd signs

Answer 1

gotta square twice

Answer 2

first time get
\[x-2+2\sqrt{(x-2)(x+2)}+x+2=16\]

Answer 3

giving
\[2\sqrt{(x-2)(x+2)}=16-2x\] or
\[\sqrt{(x+2)(x-2)}=8-x\] then square again

Answer 4

\[(x+2)(x-2)=64-16x+x^2\]

Answer 5

\[x^2-4=16-16x+x^2\]
\[-4=16-16x\]
\[16x=20\]
\[x=\frac{5}{4}\] hmm did i mess this up? lets check

Answer 6

oh yes i should be
\[x^2-4=64-16x+x^2\]

Answer 7

i turned the 64 into a 16 my mistake

Answer 8

ok better. we get
\[68=16x\]
\[x=\frac{68}{16}=\frac{17}{4}\]

Answer 9

and check is
\[\sqrt{\frac{17}{4}-2}+\sqrt{\frac{17}{4}+2}\]
\[=\sqrt{\frac{9}{4}}+\sqrt{\frac{25}{4}}\]
\[=\frac{3}{2}+\frac{5}{2}=\frac{8}{2}=4\]