Question

Need help with radical equation. Will give medals!

Answer 1

What is the problem?

Answer 2

\[\sqrt{x^2+1}+\frac{ 8 }{ \sqrt{x^ 2+ 1} }=\sqrt{x^2+9}\]

Answer 3

Fixed it

Answer 4

If you suare both sides, you get\[x^2+1+16+\frac{64}{x^2+1}=x^2+9\]

Answer 5

Can you solve it from there?

Answer 6

I tried solving it that way earlier but messed it up. Would you mind continuing?

Answer 7

\[x^2+17+\frac{64}{x^2+1}=x^2+9\]\[\frac{64}{x^2+1}=-8\]How's that?

Answer 8

I think thats's good thanks.

Answer 9

Where did you get the 16 from?

Answer 10

And could you just finish the problem please? I'm still confused.

Answer 11

\[(a+b)^2=a^2+2ab+b^2\]\[(\sqrt{x^2+1}+\frac{8}{\sqrt{x^2+1}})^2=x^2+1+\frac{2*8*\sqrt{x^2+1}}{\sqrt{x^2+1}}+\frac{64}{x^2+1}\]\[x^2+1+16+\frac{64}{x^2+1}\]

Answer 12

\[-8=x^2+1\]\[-9=x^2\]\[x=\sqrt{-9}\]\[x=3i\]

Answer 13

Thanks you so much!

Answer 14

Welcome.