EinsteinJr

Exactly. Here's your cookie, Melody:

First you must prove that this polynomial has no real roots.

(For any polynomial ax²+bx+c, the roots are $$\frac{-b \pm \sqrt{b^2-4ac}}{2a}$$ )

If it doesn't have real roots, it will always have the same sign as a, which is 4 in that case. 4 is positive, so the polynomial is positive for any real number x.)

$$n^a \times n^b=n^{a+b}$$

So $${{\mathtt{5}}}^{{\mathtt{3}}}{\mathtt{\,\times\,}}{\mathtt{5}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{{\mathtt{4}}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{{\mathtt{2}}} = {{\mathtt{5}}}^{{\mathtt{3}}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{{\mathtt{1}}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{{\mathtt{4}}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{{\mathtt{2}}} = {{\mathtt{5}}}^{\left({\mathtt{3}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{4}}{\mathtt{\,\small\textbf+\,}}{\mathtt{2}}\right)} = {{\mathtt{5}}}^{{\mathtt{10}}} = {\mathtt{9\,765\,625}}$$

One minute of arc is 1/60 of 1°

One second of arc is 1/60 of one minute of arc, or 1/3600 of 1°.

I'm ALWAYS right ! Just kidding.

My favorite songs:

• God save the Queen (I think the British Anthem is the most beautiful national Anthem in Europe)
• La Marseillaise (Yes, I love the French national Anthem, maybe because I'm French)
• La Marcha Real (No, I'm not spanish but I think that the Spanish Anthem is good... Even if it doesn't have lyrics)

I'm 26! years old. Why ?

I hope this cookie is small enough

And congratulations Melody

Precisely.

$${\mathtt{\,-\,}}\left({{\mathtt{1}}}^{{\mathtt{2}}}\right) = -{\mathtt{1}}$$ but

$${\left(-{\mathtt{1}}\right)}^{{\mathtt{2}}} = {\mathtt{1}}$$

So $${\frac{\left({\mathtt{4}}{\mathtt{\,\times\,}}{\mathtt{5}}\right)}{\left({\mathtt{\,-\,}}{{\mathtt{1}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{5}}\right)}} = {\frac{{\mathtt{20}}}{\left({\mathtt{\,-\,}}{\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\mathtt{5}}\right)}} = {\frac{{\mathtt{20}}}{{\mathtt{4}}}} = {\mathtt{5}}$$

$${\mathtt{5}}{\mathtt{\,\times\,}}{\mathtt{5}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{5}}}{{\mathtt{5}}}} = {\mathtt{25}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}} = {\mathtt{26}}$$