+96 1)
Simplify \(\frac{2\sqrt[3]9}{1 + \sqrt[3]3 + \sqrt[3]9}.\)
2)
What are the roots of x^2 - 2x + 2?
3)
Express (4-5i)(-5+5i) in the form a+bi, where a and b are integers and i=\sqrt{-1} is the imaginary unit.
+118608
\(\frac{2\sqrt[3]9}{1 + \sqrt[3]3 + \sqrt[3]9}\\~\\ =\frac{2*9^{\frac{1}{3}}}{1 +3^{\frac{1}{3}} +9^{\frac{1}{3}}}\\~\\ =\frac{2*3^{\frac{2}{3}}}{1 +3^{\frac{1}{3}} +3^{\frac{2}{3}}}\\~\\ let\;\; x=3^{1/3}\\~\\ =\frac{2x^2}{1 +x +x^2}\\~\\ =\frac{2x^2}{x^2+x+1}\\~\\ \)
I really do not see this simplifying very nicely
coding:
\frac{2\sqrt[3]9}{1 + \sqrt[3]3 + \sqrt[3]9}\\~\\
=\frac{2*9^{\frac{1}{3}}}{1 +3^{\frac{1}{3}} +9^{\frac{1}{3}}}\\~\\
=\frac{2*3^{\frac{2}{3}}}{1 +3^{\frac{1}{3}} +3^{\frac{2}{3}}}\\~\\
let\;\; x=3^{1/3}\\~\\
=\frac{2x^2}{1 +x +x^2}\\~\\
=\frac{2x^2}{x^2+x+1}\\~\\
