# Two functions intersect,solve the equation.

Given two functions,show where they intersect

$(x^2−5)^2/(x+7)^2=\sqrt{169-x^2}$

I have already tried to square both of them but I get a very complex equation and I can not solve it. I saw a guy who put Ln before and before the two sides of the equation.

• guys, should Natural logarithm is aplied herre – Rocket Apr 30 '14 at 2:38
• You didn't provide two functions; you gave one equation. Do you mean to say the first function is $(x^2-5)^2/(x+7)^2$ and the second function is $\sqrt{169-x^2}$? – Joel Reyes Noche Apr 30 '14 at 2:41
• yea, dude if you speak spanish let me know, its difficult to explain with English – Rocket Apr 30 '14 at 2:42
• Your equation is a 8th-degree polynomial. There is no simple solution for such equations. See How to solve an nth degree polynomial equation. – Biswajit Banerjee Apr 30 '14 at 3:00
• Because at best you will get something like $$4\left[\ln(x-\sqrt{5}) + \ln(x+\sqrt{5})- \ln(x+7)\right] = \ln(13-x) + \ln(13+x)$$ which cannot be solved without numerical methods. – Biswajit Banerjee Apr 30 '14 at 3:09

This equation simplifies to an 8th degree polynomial that can't be solved explicitly. Applying logarithms gives you $2 \log(x^2 - 5) - 2 \log(x+7) = \frac{1}{2} \log(169-x^2)$, but this does not simplify. As always, numerical approximations such as newton's method will get you approximate answers that @JoelReyesNoche gave.