Originally Posted by

**Luminary** Hi all.

I'm having trouble trying to solve this problem without a calculator.

The first part of the question is to solve $\displaystyle x^2-(6\sqrt3))x+24=0$, giving your answer in terms of surds. I solved this and got $\displaystyle 4\sqrt3$ and $\displaystyle 2\sqrt3$.

For the next part of the question, I need to solve $\displaystyle x^4-(6\sqrt3)x^2+24=0$, giving the answer correct to 2 d.p.

By letting $\displaystyle y=x^2$, I can get that $\displaystyle x^2=4\sqrt3$ and $\displaystyle x^2=2\sqrt3$, and from there that $\displaystyle x=\pm2\sqrt[4]3$ and $\displaystyle x=\pm\sqrt2\sqrt[4]3$, but I really don't see how I could work out the values without a calculator. Any ideas?

Thanks in advance.