Question

Solve each equation symbolically. With explanation please.

sqrt (x)+1=sqrt (x+2)

Answer 1

hint...
\[\LARGE \sqrt x+1=\sqrt{x+2}\] square both sides..

Answer 2

Im not sure but I think I should foil left side of problem

Answer 3

\[(\sqrt{x}+1)(\sqrt{x}+1)-x+2\]

Answer 4

thats an = in front of x

Answer 5

\[\LARGE (\sqrt x+1)^2=(\sqrt{x+2})^2\]

\[\LARGE (\sqrt x)^2+2\cdot \sqrt{x}\cdot 1+1^2=x+2\]

\[\LARGE x+2\cdot \sqrt{x}=x+2-1\]

\[\LARGE 2\cdot \sqrt{x}=x-x +2-1\]

\[\LARGE 2\cdot \sqrt{x}=1\]

\[\LARGE \sqrt{x}=\frac12\]

square both sides and there you go :)

Answer 6

can you do it ?

Answer 7

solution manuel says x = 1/4

Answer 8

that's correct. Well done ! ;)

Answer 9

Thank you once again :)

Answer 10

Glad to help :)