Hi, so I've been selfteaching myself maths as a hobby for a little while now. And I came across this problem that's confused me a bit. I thought I followed all the necessary steps to simplify it, but my answer book told me I didn't take it that one step further. I'm not sure how it got this final answer and my book frustratingly hasn't taught me how it came to this conclusion.
\(\displaystyle 45x^6\, =\, 9x^4\)
\(\displaystyle \dfrac{45x^6}{\color{blue}{x^4}}\, =\, \dfrac{9x^4}{\color{blue}{x^4}}\)
\(\displaystyle 45x^2\, =\, 9\)
\(\displaystyle \dfrac{45x^2}{\color{blue}{45}}\, =\, \dfrac{9}{\color{blue}{45}}\)
\(\displaystyle x^2\, =\, \dfrac{1}{5}\)
\(\displaystyle \color{blue}{\sqrt{\strut \color{black}{x^2}\,}}\, =\, \color{blue}{\sqrt{\strut \color{black}{\frac{1}{5}}\,}}\)
\(\displaystyle x\, =\, \color{blue}{\pm}\dfrac{1}{\sqrt{\strut 5\,}}\)
\(\displaystyle \color{red}{ x\, =\, \pm\, \dfrac{\sqrt{\strut 5\,}}{5} }\)
Thanks in advance! (Black and blue is my working out. Red is what I missed according to the answers page)
\(\displaystyle 45x^6\, =\, 9x^4\)
\(\displaystyle \dfrac{45x^6}{\color{blue}{x^4}}\, =\, \dfrac{9x^4}{\color{blue}{x^4}}\)
\(\displaystyle 45x^2\, =\, 9\)
\(\displaystyle \dfrac{45x^2}{\color{blue}{45}}\, =\, \dfrac{9}{\color{blue}{45}}\)
\(\displaystyle x^2\, =\, \dfrac{1}{5}\)
\(\displaystyle \color{blue}{\sqrt{\strut \color{black}{x^2}\,}}\, =\, \color{blue}{\sqrt{\strut \color{black}{\frac{1}{5}}\,}}\)
\(\displaystyle x\, =\, \color{blue}{\pm}\dfrac{1}{\sqrt{\strut 5\,}}\)
\(\displaystyle \color{red}{ x\, =\, \pm\, \dfrac{\sqrt{\strut 5\,}}{5} }\)
Thanks in advance! (Black and blue is my working out. Red is what I missed according to the answers page)
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