Question

what are all real solutions to (square root of x+5)+(square root of x-3)=9

Answer 1

\[(\sqrt{x}+5)+(\sqrt{x}-3)=9~~~?\]

Answer 2

i think he means the 5 and 3 are under the root.

Answer 3

\[Add\]
\[2\sqrt{x}+2=9\]
\[2\sqrt{x}=7\]
\[\sqrt{x}=\frac{7}{2}\]
Square both sides,
\[x=\frac{49}{4}\]

Answer 4

If square root of( x+5)+square root of( x-3)=9
\[\sqrt{x+5}+\sqrt{x-3}=9\]
\[(\sqrt{x+5}+\sqrt{x-3})^2=9^2\]
\[(\sqrt{x+5}+\sqrt{x-3})(\sqrt{x+5}+\sqrt{x-3})=81\]
Expand,
\[(x+5)+2\sqrt{x+5}\sqrt{x-3}+(x-3)=81\]
\[2x+2+2\sqrt{(x+5)(x-3)}=81\]
\[2x+2\sqrt{(x+5)(x-3)}=79\]
expand , then square both sides again